I'm sitting here with a borked laptop I've been enlisted to repair or replace. Unfortunately I have no Win7 recovery disc at hand to get a fresh install and making one out of the current state of the laptop doesn't work.
Before I go and buy a new Windows license, I'd like to find out whether or not the hardware is ok.

The two solutions that come to mind are using diagnostic software to check the hardware and/or installing a free OS to see if that fixes the problem.
So, is there some diagnostic software suite reliable enough that I could trust it in case it tells me the hardware is alright?
Having never used Linux before, is there some easy to use package that would let me try out the hardware without taking too much time to setup?

Try an Ubuntu installer CD. You can boot into a live environment which, while a little slow, is perfectly adequate for testing out the system's hardware. I also believe, if memory serves, that the Ubuntu installer CD contains a copy of Memtest86+, which you can use to check that the laptop's RAM is alright.

Perhaps something like the SystemRescueCD or Ultimate Boot CD.
Hiren is also nice.

If it's not the RAM it could be the hard drive; you can run a bootable S.M.A.R.T. tool for that hard drive brand to see the current state.Windows 7 ISOs are hosted by Digital River, Microsoft's official distributor for Windows 7 downloads, so the files themselves are legitimate (just not normally linked publicly). There is no official equivalent for Windows 8 ISOs since Windows 8 and newer are distributed through a dedicated downloader.

Thank you all, I installed Ubuntu and so far the laptop seems to be running well. I'll keep an eye on it for a few days since the issues were a bit intermittent and will probably try out some of the diagnostic tools you suggested, but right now it's looking good.

Regarding "My Digital Life": Yes, I have the serial below the laptop, but at first glance that site doesn't look all that legal to me. I'll have a closer look at that tonight.

MDL is quite a weird case actually. They are documenting activation processes, and they are providing tools to facilitate such process, but it does seem to be tolerated by Microsoft. As Arkose said though, the isos they link are legit.

And should you at any point have a question about MS products, MDL probably has you covered.

Alright, the culprit is found. What looked like an OS issue was actually a faulty hard drive. Will replace it tomorrow and hopefully not be surprised by something else after that.

Unfortunately I can't mark several post as the solution so I'll pick the first to suggest "ultimatebootcd" which I ended up using the most. But thanks again to all of you!