I've found the solution to this problem and I'd like to share it.

An old Packard Bell EasyNote R1935 (or MIT-RHEA-C) laptop with Ralink RT2561/RT61 network controller.
The Wireless card is detected, but can't be enabled.

Upon closer inspection of the messages printed by dmesg, I've noticed some IRQ issues and a suggestion to pass pci=biosirq to the kernel while booting. Unfortunately this didn't fix my problem, but it made me search the dmesg output for BIOS related messages.

This line caught my eye:
because I've had another problem with this notebook. Upon shutting down, it didn't even want to switch off, it just hang at "Shutting down" (or something similar).

Passing that kernel parameter (acpi=force) fixed the shutdown issue, but also resolved the problem with the wireless card!

So, add this to your LILO:
If you're using GRUB, I think you have to add it to the end of the following line, like this:

"acpi=off" or "acpi=force" normally fixes most issues I have with any older hardware recently. Cheers on the fix! Also replying to take off the ZRL.