I knew that i'd never get my money out of my bike, but I wouldn't mind if I had a nice, reliable bike to get me around (I don't have to have the shiniest or the fastest).  I sure didn't expect to get stuck with a money pit, thoug!  I've had one problem after another keeping this bike running.  It's a '96 and was in great cosmetic shape, but it's never run quite right.  I've replaced this, rebuilt that, cleaned this and that, but it never behaved like it should.  Every thing I'd fix would lead to something else to spend money on.  To make things worse, I went down on it last month, so it doesn't even have the cosmetic going for it anymore.  With engine problems and several dents and scrapes, how do I ever get out from under this thing?  I figure I'll just have to take a beating and sell it cheap, but if I don't get much for it I won't be able to afford anything else for a year or so.  

I guess my real question is would it be worth paying a professional to go through it and fix it properly, or would that just be throwing more money in the trash?

only if that so called professional is a good friend willing to help you go through it with beer and a BBQ for couple weekends.  (non dealership/repairshop deal)

welcome to the world of motorcycles...
 

Don't know what to tell you.  GS are kinda designed as cheap "throwaway" bikes for learners and the occasional odd ball (like us).
They don't cost much and have even less resale value, but their price does stabilize at around $1500 to $2500.  I suspect yours is pushing closer to the bottom of that range.  
If you think your GS has served its purpose, and bravely taken you thru your newbie, mistake prone, asphalt magnet stage; and think you are ready for a nice bike, you have a couple of options:

A)Call it a loss and sell it for what ever you can or what ever a dealer will give in trade.
B)Sink just enough money into it to get it fairly presentable to try to break even (what your Previous Owner did?)
C)Part it out. Might make more but takes longer.

Hope this helps...