Can i swap out the processor?

Possibly.

Firstly, what is the processor and motherboard of the PC that you currently have, specifically please.
Secondly, what is the 2.8GHz processors name?

As Lmeow said above, its impossible to know exactly without you giving us more info, specifically your motherboard make and model and also the make and model of both the processors in question.

Both processors are pentium 4. The motherboard has no identifying marks on it.

Possibly/probably. Intel made several 2.53 GHz and 2.80 GHz P4s, but fortunately most of the different generations of parts (that wouldn't be compatible) have different sockets and won't fit in a board that won't support it. As a general statement, if it fits, it will likely work, although it might run slower than 2.80 GHz (e.g. putting a 800 MHz FSB 2.8C chip in a board that only supports 400 and 533 MHz FSB chips.) The only ones that will likely cause a lot of trouble are the 2.80 GHz 478 Prescotts.

But as we've said above, if you can take and post pictures of the tops of the CPUs in question, we could probably tell you for sure.

when the computer is starting up, it will list the motherboard. You may have to press the tab key during startup to see all the stuff that loads. Take a picture of whats listed. Then google the motherboard, pick the manufacture website link, and there should be a list of cpu processors that are compatible with that motherboard.
and this thread is a year and a half old and you probably have a new computer by now

Thanks everyone, all set now.