As you may expect, we don't recommend continuing to use damaged video cards, even if they seem to work. The best idea in this case is to give it a proper funeral: screenshots from the good old days, this card hanging out with its now-deceased DDR 2 memory stick friends,  maybe even hire James Earl Jones or Lawrence Fishburne to deliver the eulogy, and put the card to rest. You never know what's going to happen with damaged electronics when they're kept in use, and you wouldn't want the tragedy to spread further.
 
The good news is that even $130 or so will you get a card that will out perform this; for an entry level gaming PC for your child, I'd recommend a 750 or 750 Ti. They're pretty capable cards for the price point, and they don't use a lot of power in the process. This makes them perfect for the uses which you outlined.