My drill can't cut a circular hole in wood - do I need a more powerful drill?
Cordless drill "handed down from your father" - odds are the battery is toast. They don't last forever. At some point a whole new cordless drill makes more sense than pricy batteries for an older drill. Not knowing what yours is or when it's from, I can't say for sure. My last one I replaced the original two batteries with two new batteries when they crapped out, and when those were toast it was clearly new drill time, given the price of things and the moving on of battery technology. 

It would probably be fine (you didn't mention what size hole, or what type of bit) for the job if it was fully functional, but old cordless drills are often not fully functional with their original batteries.