On Linux, the wallet file is stored in your home directory, in the hidden directory .bitcoin (it starts with a dot). So the full path is /home/user/.bitcoin/wallet.dat .
If you used LinuxCoin with the 'persistent' option, your data is still safe on the USB. Start LinuxCoin, open the file manager and browse to that directory. If you don't see it, it's possible that hidden files are not displayed, look in the options (i think right click > show hidden files should work). You should be able to copy the file to the root of the USB or send it attached by email, and so on...
If you didn't have persistence, I think the data is lost. Sorry.