02 GP SE Blower problem

Blower sometimes works and sometimes not. Happens on all blower settings(1-5) and all combinations of AC/Heat/Vent settings. If I leave it turned on when not working it will eventually come on while driving. If working it never turns off while driving. Will go from working to non-working or vice versa if engine is turned off and then restarted (sometimes). During the course of this ongoing problem the radio/clock light quit working. Stereo still functions and I can see the readout if the sun hits it just right.
Recently had the battery replaced.
Have manual climate control. Any suggestions? I am not much of a DIYer and do not have much in the way of testing equipment.

If the radio display doesn't come back on when the HVAC starts working, then they are unrelated.

Since you have no speeds at all, I would say it's a blower resistor. If you still had speed 5, I would say it could be an ignition switch/harness issue, as speed 5 gets it's power through the relay (which is built into the resistor) and is independent of ignition switch function.

On the radio display, you most likely have a burned out backlight bulb, a pretty common issue on GM factory radios.

Thanks for the advice. Having seen procedures for both the blower resistor and the bulb for the radio backlight these are repairs that are fairly straightforward to complete, even for a non-mechanic like me. I appreciate your quick response.