This sounds like an issue with the speedstep functions of your processor. I recently had a similar issue, but mine was due to overheating (a broken processor fan) - I would be able to load a game (like Half-Life 2) and play it for a minute or two, and then it would become laggy (around 10fps) and even restarting only fixed it for a small amount of time. It sounds to me like your computer is stuck at the lower speed, and this could be a temperature issue too or it could be something else, I'm not sure.
I recommend calling Dell, but do this first: When the computer boots up, press F12 repeatedly at the Dell logo (if you reach the Windows XP load, you've gone too far - shut down and try again) and then select Diagnostics from the menu. It will take about 15 minutes to go through the required diagnostics, and then you will encounter some buttons after it boots the diagnostic partition; choose Custom Scan (or something like that, going from memory so excuse any mistakes). Now you have a menu with a list of your system components. Head to the Fan section and run both tests, to make sure your fans are fine. Then run the processor checks. If all of those pass, then it's something low-down and maybe the Dell rep can help you. However, if one fails, no matter how small you think it is, it is a faulty component. I watched the fan test and it set the RPM on high and then tried to read the RPM. The speed read as 0 each time and the test failed, but I heard my fan go faster so I thought everything was fine even though it failed. Like I said above, the fan was in fact broken and my computer runs great now that I got it fixed (and the fan passes the diagnostic test too). If you do fail one of the tests, just write down the error number (it will be something weird like E0002:345EA, just write it down, you can even write the error message) and then call Dell as soon as you can and present that error number to them. Assuming you have a warranty, they will help you - if you don't, then they can at least point you in the right direction as far as buying new parts.
I hope nothing in your computer is broken, but it looks like you might have the same issue as I had, although you don't mention your computer running fine just after a cold boot, so maybe not. Oh, and I should also mention, I was also able to run NHC to kick the processor up to 2ghz when it was stuck at 1ghz. However the temperature quickly ramped up and NHC warned me of high temperatures, so I stopped. And like you described, the 2ghz forced by NHC was being resisted by the temperature detector in the processor trying to bring it down to a constant 1ghz, so it was an unstable 2ghz, kinda shaking between the two speeds.
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EDIT] I figured I would give you a link to my thread too, you can read my rambling and DELL-Machina's kind words, maybe it will help you. I really think, though, that you should go through the diagnostics immediately.
http://www.notebookforums.com/thread180553.html [
/EDIT]
