Because the Dell website is so fucking helpful for tech support when you don't own the machine, I can't advise a great deal other then telling the son never to touch a pc again without learning about them. I would imagine that the laptop's hard drive was configured like most laptops and pc's are nowadays with a small section reserved for the restoration process. On bootup you can press a key to start the system recovery. I'm guessing this was done in a fat or fat 32 partition which windows 98 saw and formatted. Now, Windows 98 will categorically not run or install on that spec machine, hence the problem you was getting. This sadly leaves you a bit stuck with a laptop you can't use. Now, after a quick search in google I found this :
What is OEM?

OEM stands for Original Equipment Manufacturer, and most often refers to the likes of Dell or Gateway.

So I would say that the laptop came bundled with an OEM version of Windows Vista, so that is what needs to go on it in order for the serial number on the laptop to work. Google images showed this so check what colour the s/n is under the laptop If you want more info on "aquiring" a solution do feel free to drop me a PM as software piracy discussion is not tolerated on this forum.