The carbon and gunk didn't get there from sitting.
The best way to determine whether it needs a valve job is to do a compression check before you tear it down. Too late for that in your case. Since you have it torn down and you broke rings, it needs a rebuild. The rings were probably broken because of a ring ridge in the cylinders.
A machine shop needs to tell you if the ridges can be cleaned up or if you need a re-bore.
So you need a rebuild on the entire engine, block and head.
