Without a picture it is hard to say. I would put it back in the pot, water lightly (don't let it dry out but don't saturate it either), and put a plastic cover over it to keep the humidity up. If the stem rots, then it may be a goner but you might check the roots before you throw it out.

I'll see if I can figure out how to post a pic!

I can't figure out how to post a picture in this forum but I posted two pics in the gallery forum at:

http://forums.gardenweb.com/forums/load/begonia/hpgal1217541120547.html
http://forums.gardenweb.com/forums/load/begonia/hpgal1218001527821.html

Thanks for any help!!! I'm going to re-pot it for now, but if anyone can tell me what type this is I would GREATLY appreciate it. It doesn't make sense to me that it's a tuberous begonia since there's no tuber (at least that I can see).

Okay, that is a rhizomatous begonia. Based on the petioles it looks like some form of ricinifolia (not that it matters).

First thing to do is probably cut the leaves off up to the stem. Do not discard the leaves because you might be able to start some new plants with them. Here is what I do for intensive care: get some plastic drinking cups such as the clear plastic ones (9 oz and 16 oz are great combos), cut 3 or 4 small gashes on the bottom edge of the smaller cup for drainage with pruners or scissors, add a mix of good potting soil and perlite or straight perlite to the cup about 2/3 of the way, shorten any roots on your rhizome and place on top of the surface, water well, and place larger cup inverted for a humidity dome. Place under lights or a bright windowsill and watch for any mold. If mold develops remove top and spray for mold and allow to dry for a few hours before putting top on again. Roots and new leaves should appear in a couple of weeks. Remove top to acclimate plant.

The new leaves may have enough vigor in them to start new plants. I like to use aluminum trays with a plastic lid to start cuttings in. I punch holes in the aluminum tray, fill with perlite (best choice) or a mix of potting soil and perlite, water slightly, cut the petioles to within an inch or so of the leaf and push it into the medium. Sometimes it is best to keep the leaf off the surface so it won't rot but some leaves can have their veins cut and the whole leaf laid flat on the surface and it will root at each cut and produce plantlets there.
Aluminum pan for begonia starts:

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This is a photo from last year that demonstrates the two cup method:

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Thank you SO much! I'll let you know how it goes :)

I didn't water it a whole lot...maybe this is why the leaves shriveled up and the plant collapsed? I get nervous about over watering!

Water your plant thoroughly and let it dry out some before the next watering. Make sure you have good drainage (holes and potting mix).

I understand the phobia of overwatering, but underwatering is almost as bad. A really porous mix will alleviate the fear of overwatering but then you run the risk of it drying out really fast. There is no perfect solution.

I can use just perlite in a plastic pot (I like the lettuce containers and I snip small holes at the corners) and keep a lid loosely on top. This way I can water heavy or let it dry out some. The next thing I know is the plants are pushing the lid up and eventually I can remove the lid altogether.

Here are some of my containers:

Salad bowls from Party City with 'Midnight Sun' with NO drainage so I have to water this very carefully but then I don't have to water it often.

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staudtii started by two leaves (a fellow club member rooted two leaves for me and since I put it in this container it took off after sitting there for weeks) 'Shamus' is in the back container.

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'Plum Gorgeous' on the left started by two leaves and a combo of 'Dorothy Behrends' and 'Mumtaz' on the right.

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One more question: What kind of lights are you using? I think I may not have a bright enough windowsill; especially this time of year!

I use ordinary shoplights. I buy the cheapest (about $8) I can find and ordinary bulbs (about $2 a piece if you buy a ten pack) too. Do look for 3 prong and a long cord - no sense in buying extension cords that cost as much as a cheap fixture. Years ago I bought a bunch of cheap shoplights that had a 6 inch cord. Being 3 prong I had to buy extension cords that cost more than the fixtures ($7 for the cord and $4 for the fixture). Get the cheapest 6 way outlet too plus a good 3 prong timer (not Timex but Intermatic is pretty good).

I run them 14 hours a day but you can play with how long to run them - say 12 to 16 hours a day.

This first picture was from the first year I set this up. You see there are no drip pans. I have drip pans under almost all my plants now. I buy a 15 pack from Sam's Club for around $10. I also add gravel to almost all of them as well to keep the pots out of the water (at least a ton of gravel so far). The pans may corrode after a few years from fertilizer and gravel (sand is very reactive to aluminum and will eat holes in the pans in a year) so expect to replace a few each year.

I also use pans for starting cuttings - one pan with drainage holes poked in with a knife or pruning shears and one pan as a drip pan.

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Thanks again :)

So I've got growth on the rhizome!

http://forums.gardenweb.com/forums/load/begonia/hpgal121538302818.html

And I plugged two of the leaves into perlite with some potting soil - like you said to do. These seem to be doing something because when I've lightly tugged on them they seem pretty firmly planted. Thanks hcmcdole!

hcmcdole, I am absolutely green with envy, looking at your very extensive light set-up. Wow! I have only six, but looking at yours gave me some ideas for a couple more possibilities. Thanks.

Okay, now I don't feel bad for having four lights - hopefully soon I'll have room for more!

You have a nice setup - I get the clear drip pans from Walmart for .30-.50 each and I end up using them for lots of stuff (drying seed heads just took up several)...