This is what happens when you search the sort of sites you do for your pictures.

She just says "he was getting me to click on loads of things".

"he was sending me messages to click on".

That's all she can remember, and then he said "you can't reset your yahoo password because your computer is infected with viruses".

Go into control panel, install/uninstall programmes and sort by date.

Take note of the dates.

Then load system recovery and restore the machine to before any recent installs.

If there is no restore point then manually uninstall the offending programmes with http://www.revouninstaller.com/

Ensure you remove registry, directories etc...you'll be prompted by REVO.

Don't rip the lad's ma, that's not on.

Check for other obvious stuff such as docs containing contact lists or other useful info that could have been browsed. You have to assume all docs , emails, browser history, cookies etc. on the drive are compromised.

Shows what a little bit of knowledge can do. Someone can have the gumption to google for a solution, but then be naive enough to ring up a dodgy number and follow instructions.

A virus?

Back in the day I had a virus which replaced page 1 of Google with bullshit advertises.

Weird, I would have thought even a crappy yahoo or bing search would have thrown up the correct pages first... Who else uses that computer, just your mum? It seems much more likely to me that a website popup claiming "your PC is infected etc." came first. I'm not trying to be mean or owt, it's just that however it first occurred is kinda important because you need to make sure it doesn't happen again (or similar).

You'll need an antivirus and malware scanner - IIRC the Microsoft one and malware bytes are pretty wel regarded:
http://www.microsoft.com/en-gb/security/pc-security/malware-removal.aspx
https://www.malwarebytes.org

Run those on all the pcs you want peace of mind for - should pick up any nasty stuff left installed/left behind (plus maybe any other crap that has collected over the years).

Then install and turn on antivirus and tell your mum to only ever trust popups from whatever antivirus you've installed; if the antivirus says it's dodgy/dangerous, don't click it. I've always paid for Eset for me, the wife and her mum's pcs, just cos it was always highly rated and clean/simple to use - ymmv, pick whichever looks good, I hear sophos do a free one these days, and that Microsoft's own is okay as well. Avoid Norton and especially McAfee like the fucking plague. 
Oh, and turn on the firewalls!

Thanks for the help everyone, much appreciated.

Malware bytes is very good. Had to use it last week to get rid of some shit on my father in law's desktop. It did seem to reset the browser settings to use a proxy server though (it didn't try to specify a particular proxy server, just that the browser should be using them) so I had to switch that back before it would work properly.

There are many splendid youtube renderings of scammers being strung along. Enjoyable.