W10 is unlikely to be the cause of your laptop dying, unless it made the CPU run harder and the heat caused a failure - but that's a hardware fault.
As you are buying new I would spend a little more to get a PC with more grunt - and install W10, you'll need to go there soon anyway.
4GB is fine for basic computing, 8GB is better.
A faster CPU (i3 or i5) is better, but budget is king.
If 300 is your limit, go the PB and lash out on an
external USB disk. You can use this to transfer the files from the old PC, then install Aomei Backupper free and use it to backup to the external disk - which you then store away from the PC.
cheers, Paul