as the old one did die randomly, and it is of over 10 years old already, I decided to go for a new hardware.
In fact, I found in a shop nearby a MSI Wind PC2325VHB with 2GB Ram, 500GB Harddisk, and an Intel Atom 230 @ 1.6GHz.
All I had to do, was to copy the content of the harddisk of the old server over, make sure the network card driver worked, and the new mac-address was assigned to eth0. Also, the grub-loader had to be reconfigured to boot from a S-ATA disk instead of a IDE disk.

Result: The system is screaming fast compared to the old hardware (It also uses up to 35W of power all by himself), and the move was pretty painless, compared to what my friends with their windows systems experience...