Better make sure you've connected the ground socket on the three-prong adapter to a good earth ground. There should be an eyelet hanging below the adapter. Remove the screw holding the cover plate on and reinsert it through the eyelet, then back into the receptacle.
If you have an digital AC voltmeter, check AC voltage between the larger of the two blade sockets and the ground socket. If the ground socket is below the blade sockets, the larger blade socket will be on the left.
You should see a steady voltage of no more than 3 volts or so. If you see 120 volts, your receptacle is wired backwards! If the voltage meanders, then the earth ground is not there.
It's possible the ground screw is not grounded at all. This could cause your power supply to go wacky. These things work the best and the safest when grounded properly. It may be necessary to find a proper earth ground, and wire it to your ground prong. Sometimes water pipes work, other times you need to hammer a five foot copper rod into the ground outside a window, and clamp a ground wire to that.
Or, you may find a properly wired three-prong outlet in the kitchen or bathroom. Bring a three wire extension cord in from there and try plugging the computer into that.
Just thinking about this some more, and remembered that hardware stores usually have some kind of inexpensive three prong outlet tester that will give you an LED indication of any problems you may have with the receptacle. Plug it into the three-prong adapter as you have it plugged into the two-prong outlet. Then you also may try it plugged into the power strip. Follow the directions that come with the tester. That's probably the easiest and most thorough way of checking the suitability of your AC power source.