Don't let her buy the converter. That would be ridiculous. Advice from a store such as CompUSA is not always good, because the salesmen may get commissions on what they're able to sell (whether you need it or not.) They'll always advise you to buy something.
Are the settings on the TV correct? Check the TV manual, carefully. TV instructions are often very poorly written.
Has she tried all the different resolutions in System Preferences - > Displays? Really, all of them?
What brand of TV is it, and how old?
Oh, also, check the cable connectors carefully. They sometimes get damaged.
PowerBook G4 17 1.5GHz, iBook G4 12 1.33GHz Mac OS X (10.4.8)