Only if Dell gave you a retail copy of XP, which is really unlikely. Instead they probably gave you an OEM copy, which is tied to the motherboard they supplied it with (actually, tied to the whole computer, but you are allowed to change a certain number of non-motherboard components).
If it's OEM then it's tied both in license (IE a contract you agreed to when buying/installing your old system that you wouldn't use the XP disc with a different computer) and with Microsoft's activation servers. I think you can run XP without activation for a certain evaluation period but you get lots of annoying pop ups and you won't be able to update it to protect yourself from attacks that exploit old vulnerabilities (which will happen if you connect it to the internet - no need to even download anything or browse dodgy sites!)
edit: actually, I think they've changed policy for the latter, you might be able to download critical updates these days.