CPU upgrade?

I have a Compaq Presario S3300NX,1024 MB DDR PC3200 RAM,2-100GB Maxtor
HD's,AGP NVIDIA GeForce 6200 256 MB video card.
Today the system would not boot up.When powered on the monitor was
black and the computer started to beep.I shut it down ,removed the cover
and checked to make sure the memory and video card were in right.I
restarted the computer,same result..it started to beep.I shut it down
again.This time I pressed on the heat sink and cpu. When I powered it up
this time everything worked fine.If I move the tower or cables the
screen goes black and the computer shuts down immediately.It will only
start up again if I press firmly on the heat sink and cpu before pushing
the power button.Once it starts it works great.
I think the problem is the cpu...It's a AMD Athlon XP 2600+ 333
Fsb,Socket A .The motherboard is a MS-6390 manufactured by Micro-Star
International.
Would be worthwhile to change the cpu and install a AMD Athlon XP
2800+ or 3000+ ? would it make it any faster??both are also 333 Fsb.
It's an older system but still does what is needed at home.