What do you do if nails will not go into the concrete on a carpet strip?

There are special nails to drive into concrete......Check your local Big box store .....They are made specifically to be driven into concrete and you may want to invest in a concrete fastener that uses 22 caliber loads to drive into concrete....

You have two options and I have used them both. The first and simplest is to remove all of the nails from the strip, cut it into about 1 ft pieces and glue it down with a premium construction adhesive. I use premium PL myself. This will only work right if your floor is free of anything that will interfere with it bonding to the concrete. That means no paint, drywall mud, stain, or dust. The other is one that I prefer. it is a special concrete nail system called "Aluminum drives" These are square aluminum nails that grab onto the sides of the holes. They use a special carbide bit that is double ended these have been the most effective way for me.

Use Tack Strip Adhesive. This page shows you some:

http://www.bostikfindley-us.com/products/index.asp...

tap con screws....hardware store has them.....you drill a small hole and then you can put a nut runner in a drill and put the screw down into the cement. the screws have a hex head and a slot for a regular screwdriver but, totally hard to do by hand........good luck

Why nail when there is excellent glue available?

I'd use "Gorilla" glue