There doesn't seem to be any programming for drawer release on this model, so it is likely to be a hardware problem. Look in the back of the drawer with the tray out and make sure the mechanism hasn't come apart. Check that the wires going up into the register have not been pinched or broken. Otherwise, it may have a drive fault and need to go to a dealer.
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If anyone needs an Olivetti ECR350 manual, c-tech collective have it here:
http://the-checkout-tech.com/manuals/cashregisters/Olivetti_ECR-350_instruction_and_programming_manual.html
Registerman
January 2011