If you're talking about connecting two PCs on a home network, then yes, you can.
If you're talking about connecting two home networks or home network or home PC to a work (business)network, that's called "remote access". There are services that do this, like Go To My PC
I believe there is a way to set this up without a service, but it's complected and easy to hack.

I am talking about setting up a connection from one location to another location ( which is not the same network (like in an office) Remote access I believe is what it would be. Back to the question, would the entire computer files be available to the other connection (computer) which is at another location. OR could you block it just to let only the program or file be used through the remote access?

The only thing the other PCs on the network would be able to "see" on your PC is the Shared folder, or any folder or Drive that you mark as shared. Any shared folder or drive (besides the default shared folder visible in My Computer) will have a hand under the icon, like this;

I believe you are talking about office networking.

This is my problem. I have a program that another person wants to be able to access and view. The other person is on another network about 30 miles away from me. If I were to let them have acess to my computer by means of Logmein.com or etc. is there anyway to block all files and programs except the one they want to view?

I can't say for sure, but on a standard network you cant share programs, just files. Services like GoToMyPC (I'm not familiar with LogMeIn) allow full access to your home or work PC, software and files. However, you can setup a limited user account on your PC to limit access to files and folders as well as software.

Okay thanks for your help. The person that wants to view the one program I can not trust to view the other files. So it best not to do anything like that. Right.

Correct. Setting up networks, enabling remote access and even using services like Go to my PC open holes (ports) on your network (router) Firewall and/or PC Firewall that make hacking into your system much easier.
A good secure Firewall is more important then your anti virus software.

Admins, thanks for the help with my mouse. I did not expect to recieve that much info & help!
You guys are doing a great job!!

You're more then welcome.