97 chevy blazer. Running lights work .but brake lights dont.Replaced brake switch. but still does not work.

Check the bulbs, could be burnt out. If you have a simple tester, one end hook to ground, the other end to power, have some one step on break peddle and see if there is power for the break lights at the bulb socket. If not start tracing back after checking the obvious things, fuse, break light rely, bulbs, corrosion at the bulb socket...