Spurious BIOS hard drive failure messages

I've been trying to refurbish an old Dell GMXT 5133 for my cousin so that I can replace his Packard Bell P60 for him. (He's disabled, and has no money, so an old slow machine is better than no machine.) On installing a 840MB hard drive, I found myself getting "primary hard drive failure" messages. Occasionally, the message was "hard drive controller failure"; both were followed by "press F1 to continue, F2 to enter setup."

Going into BIOS setup didn't show anything wrong. It had identified the drive and set appropriate parameters for it, though those parameters didn't always match the physical geometry shown on the drive label. However, the capacity was always correct.

Continuing (either after going into BIOS setup or pressing F1 to continue) resulted in a normal boot, with the drive recognised by whatever OS I'd booted into, and showing appropriate characteristics.

Trying another hard drive (two more, actually -- both 6.4GB) got the same results, so it's a safe bet that the drive is not the problem. A drive data cable change also made no difference.

In short -- the system runs OK. It just throws up one of the failure messages at every boot. But I won't give my cousin a machine that lies to him -- he's a complete novice when it comes to computers, but he's not stupid. At this point, I've run out of ideas about how to make that error message go away. Suggestions, anyone?