You can remove the carpet. Concrete is increasing in popularity as a finished floor. Potential problem is old glue or improper finish of concrete by original installer. There are remedies if you want to do something other than paint. Paint will basically 'cover up' most of the problems. However, you can achieve, with your current slab, some pretty amazing results with a little time and a lot effort.
Paint is one solution...but, have you considered staining the concrete? It is a lot of work compared to simply painting. I think, though, you will find it is worth the effort. Reply if you want some info on this. And good luck, whatever you decide.