Good advice as always from these experts but I'd suggest a more progressive approach. This is the moment for Dad to leave 95 behind.
So, if you can, do Richard's backup. Then get your old man onto 98 Second Edition. Microsoft have ceased active support for 98SE but there are many high street PC shops that'll sell you the clean install CD and that will Boot from the CD Drive. Shouldn't cost a lot. Likely the HD is a bit small so don't try anything more modern than 98SE and keep away from Win Millennium Edition!!
Microsoft do still have a good update facility on their Web Site and it's a simple matter to auto-download some useful patches and driver updates.