I have two CPU's linked by ethernet connection.  I keep some programs
and files on the older computer, and keep my primary programs and
files on my main CPU.  I access the old files I need through a "My
Network Places" connection.  But is there a way to access and utilize
software programs from my old computer via my main computer and
display?  In other words, I would love to be able to use the old
CPU/hard drives, but without having a monitor, mouse and keyboard
attached to each.  How can I achieve this?

You can use www.tightvnc.com (free) to do view and access the 2nd
computer as if you were there.

You could get a KVM (keyboard, video, mouse) switch
http://froogle.google.com/froogle?q=kvm+2+port&btnG=Search+Froogle to
swap between displays. This can be pricey, but there are sets that are
available that swap between just two computers. I haven't been happy
with the Proconnect. It could be I just had a defective model. If you
get a separate box, you'll need to buy cables as well.

The "tightvnc" looks like the way to go, but it appears hopelessly
complicated to make work for a non-computer expert like myself.  I
have tried installing on both my computers but can't make a
connection.  Any step-by-step directions -- "TightVNC for Idiots" ---
available?

On the computer you want to view, install tightvnc as a service. at a
command prompt (start, run, COMMAND, ok) type
NET START WINVNC
"You don't have a password" (enter one. Twice. [OK]

From the viewer PC, start, (all)Programs, TightVNC, VNCViewer (anyone is good) 
put in the IP address of your viewer PC. 
Put in the password you used above.

Have fun. 
PS: if you're not concerned with security, click on the upper left of
the viewer window when connected and save the connection to your
desktop. Include the password, and you should be able to double-click
the icon to connect quickly to PC2.
PPS: the above only works if you have agreed to associate .vnc with
TightVNC on setup (I don't think it is automatic).

you could use XP's terminal service

If the old computer isn't running XP, that isn't going to work, I'd think.

You can use the program SAMBA.downloadable from http://us1.samba.org/downloads

Binodc: 1) the link doesn't work 2) Samba is for file sharing 3) How
in the world is samba going to be easier to install and setup than
tightvnc? 4) Why choose Samba if Windows already has file sharing?

If you're not tech savy and can't setup tightVNC you're probbably
going to have to buy a commercial product like pcAnywhere.  It's
cheap, and can be had for as little as $13 from
http://www.noblepcs.com/customer/search.php?substring=pcanywhere (for
instance).