OK - I looked up the specs on the L series - which seemed to be the only match. They did not have a manaul listed by model number but only for the Lxxxr series.
You listed above that he has two hard drives, and I assume he has an optical drive of some sort - DVD or CDRW. If so, he has used the three available power connectors and has no more left. He would have to replace.
He should have available inside an ATA data cable. It would be a cable with two connectiors, one filled and one available. You would need to confirm this, although it may be academic if no power is available.
Further, if it is a SATA laptop drive that is a further issue - a major one. You would need power and data cable adapters - which in theory are simple plug ins but are not to be troublesome and not always work. An alternate, a more reliable one, for the data cable you could get a SATA pci card. That is regular mobos support them. But I don't know if there are any special issues with the Dell mobo or BIOS.
You might also inquire at the Dell forum, they might have members that have tried or done it. But you need to know whether it is a SATA or ATA drive as a minimum. And also confirm that he has no other optional or owner installed items filling up the second 3.5" bay - like another optical drive, or card reader, or something.
Another option would be to get a USB enclosure for it and connect it as an external USB drive. Obviously it would be very slow - USB speeds - and probably only the slower USB 1.0 not 2.0, but it could perhaps provide addtional storage that way.
I think that computer is older than your grandson. It has a Pentium III processor - goes back about 4 generations. By the way - here are the specs on it:
https://support.dell.com/support/edocs/SYSTEMS/dmum/specs.htm