laptops "clashing"

[#1]

My son's girlfriend just got a new laptop.  It was the same model as her father already had, but they found that they couldn't get onto the internet.  After a lot of messing around, they tried turning her father's laptop off, and got on line, but now her dad couldn't! Turned her laptop off and he gets on line fine, but she can't.
Does anyone know of a get-around for this problem?  It appears that the fact that the two laptops are the same make and model, is causing them to clash, even though they presumably have different mac addresses (I haven't checked)
John

[#2]

wired?
wireless?
fixed ips?
dhcp?
need a bit more to go on really than you've said ...
also do an ipconfig /all on each when they're able and unable to access the internet and post the results here.
i'm going to bed in a minute but i bet someone else'll be able to help

[#3]

Quote from: hulls

It appears ...

But it will be something else TBH.
Please give more details, as asked for by paulh.

[#4]

Make sure that they both have different "Computer Names"
Right click "My Computer" > "Properties" > "Computer Name"

[#5]

Sorry for the delay in replying, I've been away for a week.
The laptops were both wireless, using a Belkin router and DHCP, they were using different computer names.  (I'd though of that one).
Oddly, I also tried running ipconfig /all (to get the mac address) and it flashed up on the screen and vanished too quickly for me to see.  I couldn't get it to stay on the screen.
I don't know if it's relevant, but she's running Vista 32 bit.
I also suspect that it's something else, but can't think what.  It's just strange that they work independently, but not at the same time. 
John

[#6]

don't just do the ipconfig/all from "run"
Open a console window (run "cmd") and then when you have a command line, do it from there.