The Compaq does have a bios. You may need to find out though just how you enter it. WAG, it's hitting F2 or F10 key during boot-up. You would need to repair it as more than likely the error 1790 is a "hard error". if you have access to the OS floppies and yet another HD, you should be able to recover. Compaq back then provided "diag floppies" that covered everything that needed to be done. Having access to this is going to be your problem. A bootable floppy that had the required files is required is going the old fashion raw method. The bios access requires it boots from "floppy" 1st as the main boot device, thus the required bootable floppy and/or diskette. While you're dealing with DOS3.1, it can very well use any latter released OS like 5.0 up to 6.2(from memory). of course, you still need the bootable floppy/diskette. Compaq support may have details on all required diags, check the "legacy side" of things to see if provided but that's a long shot.
We have a 1987(circa) Compaq Portable 3, with DOS 3.1 installed. 5" floppy. A few weeks ago I used it to do a bit of batchfile stuff to show people what it looked like in 'the old days'.I've just fired her up again and got '1790 - disk 0 error' which I believe to mean hard disk failure. Is this the end of the the computer without perhaps major surgery? Can I get into the BIOS? Is there a BIOS to get into? Any thoughts would be most welcome.

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