Unfortunately, as you probably suspected, you cannot install from that disk without an original qualifying product. If, by chance, you noted the product code from your earlier disks or even better, registered it, Microsoft will send you a disk that Office95 will recognise.
I had a similar problem with my version of Office95 that came on floppies. Ugh. Hours and hours to load it and the master disk required you to uninstall properly. Like you, my machine crashed, I didn't do an uninstall and the data was not written to the master so it assumed it was a pirate copy.
I mailed Microsoft and much to my surprise, they were quite sympathetic and sent me a CD-ROM version with their apologies. I had registered the program, and there was no bother at all.
Failing that, find a sympathetic friend who has an older or full version. It's not piracy, and whilst not strictly within the letter of copyright law, I wouldn't feel guilty about it at all. You've paid for the products.
Cheers