If you suspect that the power outage may have damaged your mainboard, it is possible that the problems could be related. Either from a failing controller or other system component. It's a guessing game at this point, if that is the cause. It could probably be diagnosed with some deep log diving.
I have seen scenarios where you get a dirty/loss of power situation which leaves the PC undervolted, resulting in a semi corrupted state. I've even seen this behavior through power cycles in some cases - so do yourself a favor and cold boot this rig if you haven't. That means disconnect the power cord and hold the power button for about 20-30 seconds. This completely discharges the mainboard and all peripherals, forcing BIOS to fully re-check all hardware. You get a clean, fresh OS instance. This may help, it may not, but always start with a cold boot when trying to diagnose this stuff. It could be something as simple as a hardware/memory artifact.
Second - is the mouse a logitech? I have had a no-click/doubleclick issue on a few different older logitech mice. I think it has something to do with irregular wear in the switches they used to use. I've had sever exhibit this behavior. Just a thought. Try a different mouse with the machine and see if the issue persists. Is it a wireless mouse? Fresh batteries if so?
Regarding the network disconnects - check your system logs, see if you have any errors? Have you rebooted what I imagine is your home/personal router? Try a different cable or port? You're going to have to get creative to see where the issue is coming from. Try a different cable, then a different port on the switch to see if perhaps you can eliminate one of these factors in diagnosis. If it turns out the PC still drops the connection with a different cable and on a different port, then the PC is probably the issue.
Submitting some models and/or system build information might help...