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I would suspect that Robert Shaw would send you a whole new thermostat if you sent them a email about the problems you are having, or maybe offer you a replacement at cost, that would be far far cheaper than buying a new one. I doubt that any display that they use would be a universal one that can be bought "off the shelf"...its probibly a highly specialized, one build just for that model unit, only available by them. Robert Shaw seems to be a pretty reputeable company.
Its funny how many companies will send you a replacement unit, if you simply just ask nicely.
A display on a cordless phone died prematurely larely, and I sent it back to the manufacturer. Lo and behold...2 weeks later I received a whole new unit in the mail...surprise...surprise.