Rama: your situation with tabs coming up "page cannot be displayed" is very likely due to your dialup connection not being able to fetch everything at once, especially if there's stuff streaming into previously opened tabs. But I used tabs more while on dialup because I could be loading a link while reading a page or pages, so just try spacing things out a bit more. Pretty much what Beck said.
As for your computer turning itself off, I had a problem with that once upon a time with a a crummy powet supply. But another cause could be a misaligned card in the motherboard.
Personal story time: my aunt had a computer that would turn itself off, stay on a few minutes, only to die minutes later. I offered to look at it, but she was ready to upgrade anyway, since it'd gotten sluggish. After setting up the new one, she gave me the old one. I looked at it for two seconds after taking off the case cover, and I found the problem was the modem card was half-way pulled out of the slot. Reinserting it solved the problem. Also, reinstalling windows solved the sluggish problem.
So try opening the case and make sure the cards are all seated properly. And be sure to hold onto the metal part of the case before touching the cards to make sure you don't electrifry anything with static.