Panther makes much sense.

You can see system details by clicking on the Apple menu->About this Mac

Version is all we really need to know (OS X 10.3.6 for example).
So we can start filling in the following details, as suggested by the Forum Rules:

When posting, please include details for:
? Your Operating System OS 10.3.? need the last number
? Your version of your Gnutella ClientLimeWire 4.0.8 (I'm guessing)
? Your Internet connection (56K, Cable, DSL) (this might be important if you are on a 56K dial-up modem)
? The exact error message, if one pops up (we need this one)
? Any other relevant information that you think may help (did you run Apple Menu->Software Update . . .?)
? Try to make your post descriptive, specific, and clear so members can quickly and efficiently help you (you've already helped here: new to macs, new eMac computer, download image won't mount)

This last sounds like a problem where the download didn't complete. Since you probably used
Safari to download LimeWire, it might help to look in Safari's Window Menu at the Downloads. They usually show as complete or not.

What do you see there?

cheers