What's wrong with this iphone? How to fix it?

Its an iphone 3g. It was working fine yesterday just sitting on table connected to laptop charging and when i checked this morning it was dead… Not turned on at all.akready checked the charger and attempt to turn it on but it does nothing. Only thing it does is it will connect to computer and itunes but it won't turn on at all. Is it just that its old or is there a way to get it to turn on?

Your best bet will be to contact Apple. Since it does nothing at all they will probably suggest that you send it in for repair. However it probably isn't worth putting money into it. It would be better to look into purchasing a refurbished iPhone 4 or 4s if you have the money to do so. It will probably cost you the same if not more to get the 3g fixed.

I may be wrong. Hopefully they can tell you to try something that gets it working again, but with it completely dead it doesn't sound promising.

Its not old. If it was working yesterday you can fix it now. Just try to connect it to itunes and restore.
try to Do the regular DC recharge. You can also try it with a different pc and itunes. If it still stays the same just take it to the service. But I think itunes will solve your problem with a simple restore.