I am looking for national and regional average pricing of ON-SITE
computer services.  I would like to see documentation of where these
numbers came from.  I am trying to determine if the computer "service"
business in my area and others are High, Low or in the middle.  I am
also interested in starting my own computer services business, but am
not sure what to charge for different services.

Here is price list for Geek Squad.

http://www.geeksquad.com/_assets/pdf/GS_Phone_Prices.pdf

This is service provided by Best Buy

Thanks for the example.  I would be willing to formulate my own
averages and pay the answer price if I got 30 or more websites like
this one.  I tried looking for websites of companies, but most don't
post there price list and I don't think it would be right for me to
call them just to waste their time.

30 sites for $12.50? 
Prices range based upon who's asking for service and who's providing
service. Established companies can command $100+/hr of service, and
more, especially when dealing with servers.

With workstations, you have a huge range, depending on your clients
(business or home users). Most (many?) home users won't want to pay
anything for service, and some would say $50/hour is too high. OTOH,
business accounts can see real return on investment (downtime x
payroll for number of users affected), so time=money is a real factor.
I don't think nationwide pricing is going to be beneficial to you if
your demographic doesn't match.

You should charge what the market will bear. Look in the phone book
and ask the rates of your potential competitors. Ask if they are
storefronts primarily or primarily onsite technicians.

Make certain you cover travel expenses in your fee. Make sure you
schedule enough time to do accounts receivable. If you're making lots
of money on paper, and not collecting paper, you're not doing yourself
any favors.

In the end, depending on your expertise and clients, you should be
able to start around $50-$75/hour as a (potentially initially unknown)
solo technician working on desktops, to $100+ for server work.

Your results may vary. This is a free comment.

And I did just re-read your comment. No prices posted on the web, and
don't want to waste the time of your competitors.

Sorry to reiterate that. 

Also, you may want to specify what "region" your "Regional" request should cover.

I personally charge $75/hr on-site (with minimum times, etc),
$20/15mins remote support, $125/hr servers & complex networking,
$125+/hr for custom programming (which I farm out to a programmer
friend of mine). I also charge $85 for a SINGLE incident--however,
adware/spyware/viruses are NOT included in a single incident--unless
you want to pay PER virus/spyware found :)

Legolas-ga

Check out http://www.realrates.com/  You can search for specific
fields, skills, locations, etc. to see what rates others are charging
and salaries others are making for various services.

My rates vary widely...
I charge anywhere from nothing for a simple "goodwill" job to about
$50/hour for *residential* customers. Businesses get charged more,
averaging around $75-$125/hour.
You should ask around and see what others are charging, and you should
also charge whatever the market will bear. It's only fair..
HTH!