A power supply as in an UPS? On an ungrounded outlet those will help you with line sags but not surges. Surges above a certain voltage threshold are normally sent by the surge protector (or surge protection mechanism in the UPS) to ground but if you have no ground it does damage. Depending on the severity of the surge, the damage can be large or small and many small surges over time can cause cumulative damage.
In my case, things got worse and worse. Initially, it was USB devices disconnecting and reconnecting occasionally and then more and more frequently. Eventually USB devices were dying. Then I started having issues with drives disappearing from the SATA interface and that problem got worse and worse until I started having trouble booting because it couldn't find the boot disk. Basically, the problem was the southbridge going, well, south. Eventually, it wouldn't POST at all. I had to replace the motherboard.
I'm not saying this is the problem, but it is a suspicion based on the fact that you started having problems after moving home.
There are several ways to test if you have a grounded outlet. One is to buy something that plugs into the outlet and tells you (like
this). You can find these at almost any hardware store. If you have a multimeter, just use that. I bought mine at Harbor Freight for like $6.00. You set it to test AC voltage. Set it to 200 or higher. Read the instructions for the multimeter if you don't know what I'm talking about, or ask someone who knows how to use one. Then you put the red pin in the hole representing the hot wire and the black pin in the ground.
Here is an image that might help. If you get something like 108 - 125, it is grounded. If you get something close to 0, it isn't.
If the outlet itself isn't grounded, you may still be able to ground it. Sometimes the gang box itself (the box that the electrical outlet itself is attached to and the wires are housed in) is grounded via metal sheathing that is around the in-wall wiring, but the outlet's ground screw just isn't connected to the box. You can test this with a multimeter. Red goes on the hot wire, black touches the box. Same results as before. Something around 108 - 125 and it is grounded, nothing and it is not. Or maybe there is actually a ground in the gang box but it just isn't wired up to the outlet's ground screw. The ground will just be a thick twist of copper wires with no insulation, as visible in
this picture. If the gang box itself is grounded or you have the ground wire twist in the gang, you can hook up the outlet's ground screw (usually green) to the ground twist or another screw that you screw into the box, depending on where you found the ground. If you aren't sure, use a multimeter. There might be white wires in the box too, but these are neutral wires and not the same as a ground.
If don't have any grounded outlets in your house, you are probably just screwed and will have to deal with it like I did. My house had no ground whatsoever. In general, it is not trivial and definitely not cheap to put in grounded outlets in a home that isn't set up with any in the first place.
Be careful testing for the ground using the multimeter! You will be doing stuff with live electricity! It is safe as long as you don't allow yourself to come in contact with the hot and something that grounds you (a lot of things will). I have replaced a ton of electrical switches and outlets and many of the installs have required figuring out which wire is the line (hot power source) and the load (something served by the power, like a light), and this requires using the multimeter with the power flowing to the gang box. Just be
very careful!