Sounds like the card to me as well, do you get the same issue with the card in a different PC or tested the monitor's DVI connection on something else (this could also be the fault albeit very unlikely)
That said, the 7300 LE is an extremely weak card by modern standards so any card on the market today should be more powerful, something like a GeForce 610 or even a 210 would be a good replacement and will run fine on that PSU. Of course you may want to take this opportunity to upgrade to a good graphics card and PSU if your wife does want the ability to run games in the future.