Just replace the home button and home button controller. Even if you don't know how to work on these things, ifixit makes it really easy. It's less than a $10 fix.
http://www.ifixit.com/Guide/Installing-iPod-Touch-4th-Generation-Home-Button-Controller/3615/3
I'm assuming that's the only problem according to what you've said. Many people here have the money to "go buy a new one" but that is not your only option. Find out exactly what all is wrong and fix it. Unless you severed solder points and tore several cables, you should be alright.
Don't take anything to Apple ever, unless it was entirely caused by a malfunction and you are still inside warranty. Otherwise, do everything yourself. Replacing parts on apple products has never taken me more than an hour, from rebuilding a mac pro 1.1 to a simple ipod touch battery/home button replacement.