I've had problems running Lunar Magic in Wine that sound like the same one. I don't remember versions and stuff though and I never did get it to work. Since you've got it working on your other computer, there's hope. (And if you do, please post the fix here, I'm curious.) I suggest you compare the working setup with the non-working one. Are they running the same version of Wine? 'dpkg -l wine' should tell you what version of Wine you have installed on any deb based system (which Ubuntu is).
Then I suggest backing up your '.wine' directory on the non-working box and copying the '.wine' directory from the working version. If that fixes it, you'll know it's a config problem. If not, it's something else. Is there any particular reason you're using 800 by 600? That's kinda on the low end these days. Reinstalling generally won't fix configuration problems, because unless you use the '--purge' option when removing packages, the config files are kept (in case you reinstall). Even with '--purge', user configs (like your '.wine' directory) aren't removed as the package system generally leaves user directories alone (with good reason).
Do you have Windows installed on either box? I ask because Wine can use native Windows DLLs and other components if they're available. Configuration is a little complicated, and which components (Wine vs Windows) work better for a given situation is pretty variable. This variable is often the culprit when one Wine installation seems to work fine and and another doesn't.
Also, check out wine-tricks and see if anyone's got suggested tricks for Lunar Magic. Often installing the right bits and pieces to get something working can be complicated an wine-tricks automates that. If some DLL or something is missing on the new install, but somehow (perhaps from another program) got installed on the old one, that could make the difference.
Wishing you the best of luck, 'cause I'd like to get Lunar Magic working on my setup too. Also, in the future it may be helpful to mention Wine or Linux in the thread title. There are actually a fair number of us Linux users here, but unless they read the post, one has no way of knowing you've got a Linux specific question.