I've got the same problem with CRT televisions, less so with monitors. Because of the annoying high-pitched tone coming from them I'm glad they're going the way of the dodo.
I did do a test of which I don't know whether it counts as double blind, with a track in wav and 44.1/16, 48/24, 96/24, and 192/24 flac formats (I think from Linn records as testcase). All from the same high quality master, I played them a number of times in random order, and then checked whether I recognised them correctly. I found that 96/24 was noticably better than the lower rates, but I could not discern any difference between 96/24 and 192/24.
That said, I did do a hearing test a few years ago, which surprisingly told me my hearing was very good for my age (then low thirties). I did suffer from a sudden prolonged bout of tinnitus about seven years ago, and have repeatedly had short episodes of tinnitus after attending metal concerts (before this happened).