It’s true: The spindles on your old stair rail weren’t installed with the notion that they would someday need to be replaced, but don’t be intimidated—they can be, even if the spindles are trapped in holes at the top and bottom.
First, you need to remove the damaged spindle. If the spindle isn’t completely broken in half, finish the job with a saw. Then persuade both pieces out of their respective holes.
Next, find the proper size spade or forstner bit, and overdrill the top hole. Be careful not to punch all the way through the rail. Mark your bit with masking tape if you have to. Overdrilling the hole in the handrail will allow you to push the new spindle up into the railing and then back down into the hole at the base.
You may need to cut down the new spindle to make it fit, but mind which side you trim down. if you cut too much off one side or the other, the shape of the replacement spindle may not line up exactly with the existing spindles. If the old spindle was glued in and the bond is still strong, you may have to cut the damaged spindle out flush and bore two new holes. If you think that the damaged spindle may be held in with a brad nail, don’t use your most expensive forstner bit to bore the new holes.
To find a matching spindle, start local. Try the lumberyard closest to your house. There’s a good chance the builder of your home purchased it there. If not, the folks working there may know where it came from. otherwise you could try an online source. Here are a few: cheapstairparts.com, stairpartsnow.com and stairwarehouse.com. If you can’t find a new one, you may need to have one custom made by a local wood turner.