Have you called your ISP and had them reset your modem from their end? I had been having that same problem as well. Says I'm connected, but no connection. Not even wirelessly. So, I called my ISP, they would reset, I'd jump thru all the hoops, and nothing worked, so they'd set up an appointment for a tech to come over in the next day or 2. A few hours later, for no reason at all, the internet would work again. So, I canceled the appt. I went thru this 3 times and they finally decided it was a problem with WinXP, noting that others had had a similar problem, including their XP expert. So, when it happened again, I decided to do a repair install of XP and have been pulling my hair out since. I was missing a great many files the first time I tried to do a repair install, and there was no repair option.
I started out using a different disk than my original, which had the wrong product key written on the outside of the sleeve. It wouldn't accept the key. Perhaps because it was an upgrade version and the key was for a retail full version.
I ran all the diagnostics also, with no luck. I can say that there were some "missing or corrupted files", including ntfx and catroot2. You also might get a copy of Memtest86 (download free) and run that overnight to make sure it's not your RAM, as this is a possibility. The other possibility is that you have 1 or more bad sectors on the hard drive. You can go into the Recovery Console and copy/replace the missing/corrupted file from the cd without needing the product key.
Because you don't have internet access on either system, you will have to take a blank cd, or a thumb drive to a friend and download the needed files. I would not advise spending money on diagnostic software, tho. To use the cd or thumb drive, you might need to go into your bios and reset your boot sequence to allow the cd rom or thumb drive to be accessed first.
Hope that helps.