Bicycle Mechanics - Newly acquired bike, chain issue?

Everyone on here seems extremely knowledgeable so hopefully you can help me out. I recently acquired a bicycle from my aunt that she had won in a raffle about three years ago. The bike was ridden for maybe 5 minutes after the win and then stored in a garage ever since. The bike is a Quasar Bounty (some cheap retail store brand I assume) and has a 3 gear setup (H and L settings for each gear set). Lately when I'm in the middle more commonly used gear setup (one in H, one in L) and try to stand up and pedal to get some momentum my bike makes a "pinging" sound and the pedals slip forward about a half rotation. Needless to say this kicks my feet off and causes me to lose all momentum on the hill. I've re-oiled the chain (assumed it couldn't hurt since it sat so long) but still no change. I'm hoping it was just a cheap assembly job and maybe something just needs adjusted. Please help me out, I'm itchin to ride.

CLIFFS:
3 year old bike that was never ridden has pedal slippage when pushed hard (up hills, standing up and pedaling). Trying to not die, help me out!

*And if pics are needed of any of the setup, let me know.

I hate to show my ignorance, but from your description, I'm not really sure what kind of gearing setup you have. What you described happens sometimes on geared bikes if the cassette is worn out (been there, got the scars to prove it) but that shouldn't be the case for you. OTOH, you may have an internally geared hub.
http://www.geocities.com/cyqlist/saam.html

I am also confused about the gearing. Pictures would help explain your bike I guess.

Well I took the liberty of taking some pics to show my gear setup as well as the results of trying to backpedal (the massive slack in the chain). Perhaps this will help the diagnosis.
Gears:
http://img177.imageshack.us/img177/3744/04hr8.jpg
Rear Closeup:
http://img387.imageshack.us/img387/7738/02ai5.jpg
Front Closeup:
http://img220.imageshack.us/img220/1938/03qi8.jpg
Left Gear selector(same as right)
http://img220.imageshack.us/img220/5684/05rh6.jpg
How the chain sits normally:
http://img295.imageshack.us/img295/5607/01cw6.jpg
As I backpedal:
http://img295.imageshack.us/img295/906/07kh7.jpg
http://img235.imageshack.us/img235/5632/08qb6.jpg
After the peak of slack it springs back to normal and then repeats. Oh, and it backpedals fine if it's upside down.

Bump!

What shown in the picture indicates either (1)The rear cluster is not turning freely and/or (2)RD not turning freely.

(2) is relatively easy to fix. Take off chain, u will feel it with your fingers whether the two pulleys need servicing.

(1) is relatively tough to service. Again take off chain, turn it with your hands it should spin fairly smoothly, if not u need to disassemble this thing, re-grease, re-assemble. Better left to your LBS.

Well I messed with the front and rear derailleurs and now have it so that it won't slip out of the mid range gear but I can't access high or low gears now :( . At least it's been a learning experience, lol.

If you can't access high or low you likely moved the indexing adjustment too far. At first glance at the derailer I'd say that something isn't spinning freely like jsmithepa mentioned. Check out Sheldon Brown's site for derailer adjustment http://sheldonbrown.com/articles.html or Park tools http://www.parktool.com/repair/

Both are very informative sites and have helpful pictures and diagrams and such.

The derailer isn't something to be afraid of, but many people are.

Good luck.

Thanks for the links! I'll definitely read up. I just got done re-adjusting by feel again and went for a ride and the middle gear never slipped! I'm guessing that the cheap cost of the bike probably reflected the low build quality as well. For some reason it seems to have lost a little of its resistance(lower top speed) but for the stuff I'm riding it's not a big deal. I can't thank you guys enough for all the help! If this bike can just get me through this year I'll hopefully get something nicer next year.

If you want to fully fix it, it shouldn't bee too hard, especially since you've gotten this far. Read up on Sheldon Brown's site and Park tools, and you're good to go.

Thanks for all the help guys! I followed the instructions today and got it shifting smoothly with no slippage. Can't wait to go hit the trails this weekend!