This Dell computer has a Pentium 4 processor with 1GB of RAM.

Another computer in my house is a Hewlett Packard with an AMD Athlon
2200+ processor. This compuer also has Windows XP. This computer only
has 512MB of RAM and runs faster than the Dell. I know the problem is
not what has been installed on the computer because I have just
purchased the Dell.

What is the problem? Please Help!

different CPUs optimize different operations.

Also, the bus speed may be different and the hard drive access times
may vary, you haven't provided enough info to give a specific answer.

What is the cpu on the pentium?

While the above 2 posts have good points (not enough info) also
consider the fact that Dell installs lots of programs that you don't
need that might increase the boot time. When my friend got a new dell
computer...after I formatted and re-installed XP (thus erasing all of
dell's software), it booted up much faster.

You should provide more details - e.g. detailed hardware configuration
of each computer or at least exact model names. Generally, computers
with "mark", like IBM, Dell, H-P etc., are equipped with weak hardware
except processors and HD storage. One of the most important part of
the computer is motherboard, and I can't even see motherboards
descriptions on Dell pages. You didn't clarified what do you mean by
"runs faster" - if you mean Windows XP speed, then the slow HDD/ RAM
may be a problem. If you are talking about games, then the graphics
card can be an issue, because cards installed in such computers are
real garbage if you look at the price of the whole system. I suggest
you to run 3D Mark (http://www.futuremark.com/ ) and SiSoft Sandra
(http://www.sisoftware.net/ ) on both systems and you should find
their weak points.