Bicycle Mechanics - Stripped threads in bottom bracket shell!

I had a really stiff BB(107 x 68) in my Giant TCR (alu frame). Got the left side out but the drive side is more... problematic. Somehow managed to turn it the wrong way by putting the tool in a vice and turning the frame. I turned the right way but the BB remover, vice, bench, workshop, Planet Earth turned the wrong way... Yes i feel stupid. Result is that the BB cup (the bit attached to the cartridge) now turns BOTH ways and wont come out no matter which way i turn it. It made a sound like a herd of elephants as i forced all my might on it. Now i can't get the bugger out. What does one do in this situation? I know you can work around it if you have an empty (stripped) shell, but i still have the old one in. I have a Stronglight BB ready to install and don't mind Using a beer can shim or even welding it in place with PBweld or even tapping a new thread and buying another a 68mm+ BB etc. But the fact is that the old one is still in there.
I worry that the LBS will, after laughing at me, tell me to get a new frame as a pennace. Can i hammer it out? Drill it out? What tools or techniques would they use?

Look around, there was a thread about this recently.

But I'm afraid you're screwed. err.. not screwed? I'm so confused.

There is little chance you stripped the whole BB by tightening it too much, but you may have done some dammage to the shell if it's an alu frame. You need to put it back in the vise and turn it so that you are turning the BB clockwise(hint turn the frame clockwise). Keep turning it, it should really come out. Ignore the elephants. You may try some DW40 on the inside of the shell to help. If you still can't get it out you are either weak or you are screwed.

This is the method that a bike shop will try and if it doesn't work they will tell you your frame is scrapped. If the drive side threads are toast and can't be adequately rethreaded your frame is toast again. you can get away with a "shim" on the non-drive side using a cartridge BB as this is effectively what the non-drive "cup" is doing anyway.

Get a new frame.

Try turning the cup the "right way" but pull firmly away from the frame on the spindle end as you do. That may make what ever is left of the threads catch enough to unscrew themselves.

If the shell is still undamaged other than the threads, it can be reamed to remove the remaining threads and rethreaded to Italian threads which are larger in diameter than English.

Is the BB stiff, as in "brand new and stiff", or is it "old, broken, and stiff"?

If it's brand new, I'd say give it time to break in before you decide to remove it.

I also find it kind of implausible that you would be able to break loose ALL of the right side threads at once! There must be something else wrong.

Given that it's an aluminum frame, I'd say your chances of causing a lot more damage to the bottom bracket shell are pretty high if you try to whack your bottom bracket out with a hammer. If it were a steel frame, I'd say go ahead and try a hammer as long as you accept that you might damage your already messed up frame some more.

Thanks fellas, I just had an idea - taking Hillriders suggestion, I will try making a rig with G-clamps to put pressure on from the other side and then turn it the right way. Might catch what ever's left of the threads. I only turned it 3 or 4 full turns before i realised my error so there should be something left... I hope.
It's stiff as in old, worn and stiff. It all still works fine, there's just a bit of wobble in the cranks because the bearings are worn. An alternative is to just ignore it till i get a new bike.

Once you get the old cartridge out, try to have the threads retapped. If that fails, there are cartridges that thread together, not to the fame.
http://www.jbimporters.com/web/images/new_400/20960.jpg

Quit now before making things worse. There's still a bit of faint hope that the BB shell isn't toast. If there's a decent mechanic locally, have him check it out. Sometimes there's enough metal left so that threads can be chased and saved, usually not.

If it's stripped you have 3 basic choices:

1- tap it to Italian 36x24 and use only those BB cups made for Italian mixed with 68mm spindles made for English.

2- use threadless BBs, such as the one shown by a poster above.

3- if it's a valuable frame, a skilled welder can build up the ID and then re-tap the shell so it'll be as good as new, except probably for some scorched paint on the shell. Note this is a skill job, and only a small percentage of shops are capable of doing it.

If no one locally can save this frame, PM me your address and I can suggest a shop or two.

Another option:
The low end Shimano cartridge BB that came in my 1994 MTB installed "backwards". It installed from the left and used the plastic sleeve on the right. The model number is BB-LP20. (Note that the current LP28 installs conventionally from the right.)

The OP still has good threads on the left. Therefore, a NewOldStock LP20 could be installed. Problems are: finding one, it might have only come in a 110mm width, and the flange on the left might be a problem with some cranksets.