you can get access to the chars but it requires some work. The old registry is not needed but you need to know the exact computer/host name your old pc had when you saved the chars. Without the correct name you are out of luck.
1. you need a Diablo installation that still uses .drv format, 1.07 or older. Either downgrade your install or do a un- and reinstall, then patch it up to 1.07 manually. Don't patch it via b.net, you get version 1.09 this way. For older patches goto http://ftp.blizzard.com/pub/diablo/patches/
2. put the .drv files into the old save directory (was \windows\system i think)
3. start Diablo, select Multiplayer on Direct Cable Connection and see if you can access your chars. If you can't you need to change your computer's name (requires reboot) until you can.
4. upgrade Diablo by connecting to b.net. During the upgrade your .drv files get converted to .sv files into your Diablo directory.