Bizzare internet access problem

[#1]

Paul B, thanks.  I've tried going through all the steps again, but with no luck I'm afraid.  I was confused by the screenshot too, but I'm way out of my depth with all this stuff, so was hoping someone wiser could enlighten me.  I'll attach the new screenshot again, which despite going through the steps again still gives no IP address - I don't understand!
I'll the new screen shot in the next post.
For interest I've tried adjusting the MTU setting too.  It's had the joyous effect of speeding up my connection but after 8 minutes it still just keels over. 
I've also tried checking all the boards, swapping the router socket, etc, all to no good effect.

[#2]

Hmmm, now I can't remember how I attached a picture last time.  I'm sure it gave me an option to browse, but it doesn't seem to be doing that now.  I'd better go to bed and try again tomorrow!

[#3]

I would personally just download a "Live" Linux Distro and give that a try.
James Barlow

[#4]

The fact it works for a while then stops confuses me, otherwise I would have suggested looking to see if the 'hosts' file has been corrupted or hijacked. Have you run any antispyware scans (adaware, spybot) recently?

[#5]

Can you still see any of the PlusNet DNS machines when it goes bad? Use ping to check if you have access.

[#6]

Just a guess further to the different info you gave I'd rather suspect first a hardware issue.
Note that in your previous post the winipconfig picture shows the IP configuration of your PPP adapter, not your Ethernet card. It might worth to check that in your Internet Options/Properties, the Internet Connections tab shows ticked the "Never Dial a Connection".
As a first test and prior to further tests I would confirm the problem appears even without the other PCs connected to the router.
Now, with preferably the other PCs still off, in order to discriminate the hardware issue, I would run the following tests one by one:
  i) replace the cable between your PC and the router if this is a wired connection -you could simply use a cable of one of the other "sane" PCs
  ii) I won't consider here to change the port on the router as you indicated this was already tested
  iii) in your "faulty" PC: re-plug you Ethernet adapter in the same slot and re-do the test with another slot, same type of slot obviously
  iv) in your "faulty" PC: use an Ethernet card of one of the other "sane" PCs
  v) in one of the "sane" PCs: use the Ethernet adapter of the faulty PC
If iv) and v) pass, just keep it like that! Though that might not have cleared the HW or SW issue.
If iv) fails and v) passes you may suspect a software problem or a serious problem with either the CPU board or the Power Supply in the "faulty" PC. Re. a PSU issue, first try to remove other boards and re-install the initial Ethernet card  to check the PSU is not overloaded. However, if you have well maintained your PCs -you're still with Win98 after all- my "preference" would go to a SW issue
If iv) passes and v) fails, I would suspect an actual problem with your Ethernet card.
If test iv) fails and test v) fails you may suspect a double fault case in the "faulty" PC: Ethernet adapter, CPU board, power supply are the more likely though a SW issue is still possible on the "faulty" PC.
Do you have to reboot to get back the connection as normal or it just happens again after a while the PC still being switched on?

[#7]

Just wanted to say thanks to everyone who has tried to help with this.  I've tried all the suggestions but aren't any further forward.  So, I'm going to give up and go for the big rebuild.  Thanks anyway.