Since when is tape unreliable?
It sure can be, especially the lower end stuff like Travan. Where I work we have over 300 remote sites, which used to have TR-5 tapes and drives that failed continuously. We replaced all of them with a local rsync to a different partition with snapshots going back a week, along with a remote rsync to a bank of servers with snapshots going back a month. We had to shell out some cash for the backup servers and some dev time for the scripts, but the savings from not buying tapes paid for them fairly quickly. The local rsyncs take the place of tapes, while the remotes provide secure off-site storage. We have been able to rebuild branch office servers using data off the backup servers with no data loss and minimal downtime. Hard drives are cheap, fast and reliable. I honestly don't understand the appeal of tapes.
My full solution would be a fanless rig, with RAID 1 for full redundancy of disks so if a hard disk fails, it doesn't take your data with it, and weekly backups to DAT tape stored off-site. Then I'd use a pair of power supplies, using a diode to prevent power from one from getting into the other, and a zener diode or 78 series linear regulators to ensure a failing supply can't overpower any one line. Then, from my little power circuit, the two power supplies would feed the one motherboard, which would be underclocked at reduced voltage. It would have the highest possible amount of RAM in it, because that would reduce the writes to the hard drives.
On the software side, I would consider hosting the DOS app on linux using an emulator such as dosemu or dosbox. The OP's dad would have an environment very similar to what he's using now. I would probably use Debian stable for both boxes, which has very long release cycles and is very stable.
With linux comes the option to replace the DAT tapes with an off-site rsync over ssh. If the main box dies, you'd be able to just swap in the backup box in a couple of minutes. If the data set isn't very large the mirror will complete in a couple of seconds. It's very easy to do:
Create a RSA public/private key pair: ssh-keygen -t rsa, press enter at the password prompts.
Copy the public key to the remote box: ssh-copy-id -i ~/.ssh/id_rsa.pub remotebox.
Have a nightly cron job to push the files: rsync -ave ssh --delete
For bonux points you could even throw in snapshots.
I'm backing up hundreds of partitions this way at work, each with snapshots going back a month. Tapes are slow, unreliable and expensive. I would not use them for any purpose.
The end of labor is to gain leisure.