You sure the dvds were 18 years old? I'm not sure there were even consumer dvd writers available around 1996. Perhaps you meant cds?
I actually had really good luck with my burned cds from around 1998 or so. I was able to read all the data off of them recently. A couple had to slow down a bit to be read, though, so there must have been some sort of degradation. Wonder if it could be more related to the burner you used or maybe the reader you used to try to read them? (Also, I can suggest ddrescue for recovering from cds/dvds if needed. It came in handy when I was recovering a scratched cd with info on it that I really wanted. I used it over and over with a couple of different readers to get a complete image of the data.)
Your hard drive suggestion sounds exactly like what I use. All the data I've read from old cds/dvds I now store on hard drives. I use SnapRaid to create a couple of parity disks. (So I can recover from up to two disks failing. Plus, since it isn't online raid, I can fix deletions and other problems as well.) I occasionally backup onto external hard drives utilizing SnapRaid again and then store them in a firesafe at another location.