The clock removes from the trim panel easily, two screws once you remove the panel. The panel just pries out (use a screwdriver with tape on it, it has tabs all along te edges). You can pick up a used clock on eBay for maybe $20-50 if your patient. Try car-part.com and getusedparts.com also. Your 2001 model clock should be interchangeable with any clock from any 99-02 Solara but check the pictures and connector first.
If your apprehensive about removing the panel or anything, get ahold of a Haynes manual at AutoZone or the like, or go to the parts department at a dealer and ask for a breakdown prinout with the diagrams of how the panel comes apart.
Also, when I disconnect my clock, my turn signals stop - though with yours it's probably just the screen part that's dead.
PM me if you need help finding one or replacing it

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