You should get the grounding issue fixed, but the only "fix" for this I know of is to use a GFCI outlet and label it with the sticky labels that say "No Equipment Ground."
However, not ideal and most surge protectors won’t work correctly in this state. This will however save your ass in case of a short to the chassis.
I’d suggest you get a cheap-o 3 plug tester like this one and validate that it’s wired correctly, or not, and that the Neutral to Earth value is 2V or less. Either of these not being true call an electrician. You might also just want to check the outlet. It could be the ground wire just came loose, or it might have bee your first surge strip was faulty. Good to have around especially in a home that's new to you. Test everything, trust nothing and maybe look at my blog for ideas on good AC for the frugal audiophile