|It should not make any difference how the jumpers are set, except some older bioses won't detect the drive at all if it's set to slave and is by itself on a data connection.|
The drives should be detected fine with no jumpers installed.
Normally, when a laptop has only one drive, you only install jumpers when you connect it to a desktop computer and even then you may not need to.
One thing I find odd is Dell lists firmware updates for the hard drives this model could originally have come with under IDE and EIDE drivers:
(Drivers and downloads - Inspiron 1500)
I checked out the hard drive models -
They are all ATA 100 and either 4200 or 5400 rpm.
The Fujitsu models listed there are set to master when no jumpers are installed. I don't know if that applies to all laptop drives, but it would probably be either that or cable select in all cases.
If your initial problem drives are 5400 rpm the bios should have no problem detecting them, but if they spin faster it might.
If your problem isn't heat related, then it could be caused by a buggy bios version.
The currently listed bios version A32 has nothing in it's Fixes and Enhancements info that would indicate a problem with the bios detecting hard drives while booting.
However, newer bios versions almost always include all the Fixes and Enhancements for all previous bios versions.
File Versions: Dell Inspiron 5100 Dell System BIOS - Previous versions
Click on a version, then the link beside Plain Text
Click on Fixes and Enhancements
If you see anything in those notes that indicates flashing the bios should fix your problem, then flash it with the A32 version.