Low quality surge protectors are just that, low quality.
Go out and invest in a name brand surge protector. APC is a good brand that I've always had good experiences with. With the storms that we get in the fall here in Vancouver, I know for a fact that my computers have been saved by these surge protectors. I've had one for 4 years now! Definately worth every penny.
Another possible cause could be a faulty power supply or an under powered system. Some companies try to cut corners on this, and they don't seem to remember that todays computers are drawing more and more power. Go back to the store that built it and ask them to check the power to the system while it's under load (basically while it's doing a lot of work).
As for RAM, 128 isn't ideal, but if it's what you have, then it'll work. That shouldn't be the cause of random reboots.
One last thing to check is temperatures. Some computers will turn themselves off if the temperatures inside the case rise too high. Download Hardware monitor and run it to have it check the temperatures of your CPU and hard drives.
Link If the temperature of the CPU is over 45 C when you're not doing anything, it would be some cause for concern. If at any time you see it rise above 60 C, turn off your computer immediately and have the computer store check it out immediately.
I'm afraid I'm not too much help when it comes to your internet problems. Sorry.