Okay, my thoughts are your problem, (some of this is derived from my experience from GMing a D&D campaign, but I think it still applies)
also, great comments so far, good suggestions all around, but here are some more suggestions, sorry about the length ahead of time, (I get to rant, YAY

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1) Overpowered characters can be a real problem, just throwing something bigger at them is also a problem. the problem IMHO comes from when one player is really powerful, and the others are not. This means the game, or combat boils down to that one person, therefore you no longer have a team.
The best way to deal with this IMO is to have a nice long talk with that player and try to convince him that having a unkillable character that can do everything really well is just game breaking, yea it's cool that their are those loopholes and they found the coolest exploit, but this is a game about semi-normal people that are not gods, and the game is about ROLE-PLAYING, not making something that looks really cool on paper. The game itself is about interacting with the people, story, world... etc.
the next thing is that IMO the edges/flaws are just for min/max players. If a player wants a edge/flaw, make them come up with a good in character reason why they want it, if it is not a natural thing, how they got that edge/flaw, this can also help flesh out a character. also make every egde/flaw by GM approval (basically approve their characters and make sure their math is correct, I know it is lame, but I have know people to go through the rules, read it a certain way that is really advantageous them, but not quite the right reading and make mad bank off of it.)
Also, look up the Becks v.2, character generation system, it works wonders at making the party less powerful. My current GM did this with us, and allowed us only 375 karma (look up becks, but basically you buy everything with karma,includingg money, skills, and attributes) when normal characters get 425. And let me tell you that 50 karma makes a big difference. All of our characters are way less powerful then a normal starting char. My rigger started out with lvl 1 VCR, and a unmodified (except for rigger controls) ford americar. It really sucked, it made me really make my character better then he needed to be outside of the vehicle. Also, it made us really scarred of just about everything, which btw really makes the game a lot more fun, when you are worried your character is even going to live against the sprawl gangers, hehe it makes things interesting. SO yea, this method worked really well for our game, and it leaves a whole lot of room for improvement. (I have so many plans for my character, he needs so much money/karma...)
2) whiney player? hmm, not sure on this one, other then just talk to him, and reward him when he thinks of innovative ways of dealing with his problems. Also, try to show him that characters with flaws (not the rules ones, but with character flaws), can be really fun to play. I once new a character who played a fighter (in D&D) with one hit point. He was the greatest warrior in the world, until the bear tore his head off, and basically we all just laughed really hard at this. I am not saying laugh at the player, but show how having character flaws, or being ineffecutal in some areas or losing some things can turn into something positive. Make the dude look at the bad circumstances as an oppurtunity. I think the idea of getting revenged as suggest by FrostyNSO, and plus, let them grow to like a character, care for that character, and really be invested into it. This can be done by trying to flesh out the story/background, also have the players interact in character. Try to get them to imagine that they are in the characters shoes, and bring the experince of the game more alive. Describe the situations they are in with rich detail, and try to communicate what you are seeing in your head to your players. Invole them in combat more by not just asking for dice roles, but ask them how they do that action, have them describe how they hit the other character, have them decribe what they do in rich detail. And again, karmic rewards for those that use their imagination, and really get into the game.
If you can get them on the edge of their seat waiting to see what happens next all of their eyes on you, then you know you are in the zone. At that point, the characters are more then just some stats on a sheet, they are a real person, in your and theirs minds. And that is the key IMHO to really enjoying role-playing.
(sorry didn't think I would talk this much so I will try to wrap it up, and please tell me if this helps...)
3) backstories? yea, ask them the million questions, ask them to create the background so they and you can understand how the character thinks, and why he does what he does. Again, I think having a good background is one the many keys to making a character more then just stats, but a person, that the player then cares about what happens.
If they say they are a orphan, then they have like 30 brothers and sisters, right? make them develop the orphanange and explore what it was like growing up there, and what not.
By making them care it makes them think about the mistakes they made, (I once had a troll character that had a little sister, said sister was kidnapped and used against me to basically make me give one of the other PC's and some information up to the kidnappers. I tried to communicate to the other players what was going on, but I was being watched and there were other things going on, so I could not speak plainly. It ended up by my character taking a serious wound from another PC sniper shooting me in the back, the kidnappers shooting my characters sister, and us losing any trace of them. I mulled this over for weeks, and it still bugs me, I keep asking myself, what could I have done better?
If you can get your players to do something like that, then they won't want to just retire their characters so readily.
4) premade adventures. Great way for a new GM to get used to things, and really just explain to them that GMing is really taxing, stressfull, and hard, and you just really want to play and enjoy yourself for once. I GM said to me that he missed playing and just wanted to play some, thus I am now running Survial of the Fittest for my group at the same time he is running his, and we switch off each week. This makes it fun for everyone, gives you a break and them a glismp into your world has a GM, hard isn't it.
Also, just talk to them, if they are mature about it and willing to listen to you and maybe you can talk to them about what you can do better has a GM, and what they can do better as a player. Doing this can really help out the game, and the levels of fun for everyone. Also, try to show them how playing the same basic character idea (i mean personallity wise) everytime can get really old. I knew one player that just loved to play a dick, nice guy in real life, but a real dick to every NPC I had in my campaigns, plus he also just wanted to wack and kill stuff. IMO his character was not a real character, just a collection of stats, thus not fun to GM and deal with.
There I hope that is enough matierial for you to get something out of it.
and always remember, the point of the game is to have fun, if it isn't fun, then what's the point?
amadeus