Dear Google,  I had purchased a web address about 8 years ago, then
stopped paying the fees.  I tried to see if anyone is presently using
it. It does not appear to be active.  How can I investigate, if the
web address can be repurchased?

First do a check to see if the domain name is still in the public
arena. Click on this address https://freehost.ie/cart/index.php enter
the domain name and use the checkbox for the domain extension.

If the domain is ?Available? well then it?s available to purchase if
it?s ?Not Available? then the words ?not available? will be a
hyperlink which will show you the new owner information details and
where the domain name is hosted.

If you want to find out who owns a web address, called a 'domain
name', you need to use a program called 'whois'.  Searching on Google
for 'whois' brings up lots of websites, one of the better ones being
http://www.betterwhois.com/ or
http://registrar.verisign-grs.com/cgi-bin/whois

It's not a simple as whether the domain comes up as 'available' or not
- sometimes a domain name may have been bought but is currently
'expiring', that is, the owner hasn't paid to renew it but has a
chance to get it back.  There are certain stages of expiration, more
info can be found at http://www.igoldrush.com/expired.htm

If the name is expiring, you can use http://www.pool.com/ to make sure
you get the name back when the name eventually expires.

Hope that helps!

Just to clarify what neave-ga is saying. It is a case of the domain
simple being ?available? or not. You can?t be nearly pregnant, you
either are or are not.

When a domain name expires the owner has a period of time after that
to renew the domain, this is known as the ?grace period? (about 40
days) if memory serves. After that, the domain goes into what?s known
as a redemption period (about 70 days). The owner of the domain can
renew the domain at any point during these two periods, however, there
is an extra fee to take it out of redemption.

To summarise, when a domain name comes up as ?unavailable? you will be
able to see the expiry date of that domain, so you should be able to
work out when the name will be back on the open market.

What's the domain name? (I'll bet you'll pay more than $5 when I offer
to sell it to you.) Just kidding, of course.

I suggest: 

Start with Network Solutions (netsol.com). From your question I gather
you are not the techie some of these other people may be. I may draw
fire for this, but although Network Solutions costs a little more to
buy domains from, they are friendly, reliable and not averse to
holding your hand through issues. I think you can even ask about
availability and buy a domain over the phone.