Alright, I think I've found a cure to this disease. It's been a couple of days now, but I wasn't into rushing out posting something I was not even sure about thus I decided to take the time to make sure that this workaround really did do the trick. And to be clear, this problem PC has now been happily running Linux Mint 5 Main Rev. 1 since a couple of days ago.
First of all, I must state that I had no idea as to what I was doing. It just came to my mind in a blitz. This may sound rather odd to you, but it did do the trick. I simply swapped the RAM module prior to booting off the live CD; it originally had a modest (i.e. not very popular) brand DDR266 module in the slot which incorporated Infineon chips. I took it out of the slot, and put mine in. The replacement module I used was a Transcend JetRAM DDR400 stick which used Hynix chips. Both of them were of the same capacity (1GB).
I then booted off the live CD, ran the installer (whilst keeping my fingers crossed)
and presto! It completed succesfully.
I was then greeted by mintAssistant upon first start of the installation. Having toyed around with it for about half an hour, I turned the computer off to put the old stick back in the slot (and took mine out), and see what would happen next. This led me to another surprise: Mint started up flawlessly with the old stick in the slot, as though it had liked the stick in the first place! How weirder could it possibly be? Less than an hour and a few tinkering with some applications later, I officially stated that the PC had been officially Mint-ized.
To make sure that the RAM module really was the culprit, I then tried to run the installer again, with the old stick in the slot. The result was predictable: it wouldn't run. In conclusion, using the old (DDR266, Infineon chips) module kept the installer from running, although the OS itself would run normally with it once installed. I never thought that the installer could be overly sensitive to even the smallest details.
I'm aware that not everybody has spare components lying around the house, but I thought I'd just share the story here anyway.
Edit: I had also upgraded the BIOS to the latest version available at ABIT's site before attempting this silly last resort.