I sold stock in 2004 for which neither I nor my broker knows the
original purchase price.  I purchased several blocks of the same stock
over the last 18 years through employee stock option programs and on
the open market, the earlier purchases have also split several times. 
My current broker was not my broker on any of theses purchases.  If
the IRS is capable of tracing my purchases/sales, is there a place I
can go to figure out the cost basis for the stock I sold?

Here are a few quick references that may help you get started. If you
were willing to post the name of the specific company, it might help
the researchers to focus in on the most relevant sites.

(1) One well-known resource frequently cited and/or interviewed on
CNBC (though not free) is this site:

http://www.stocksearchintl.com/cost_basis.html

(2) Some companies have calculators on their own web page (under
investor relations) to find that information. You might also contact
your "investor relations" or "corporate communications" department
directly to assist in researching your open market prices as of the
day you purchased the shares, or even your "employee benefits"
department (since you are an employee) to get the stock option
information from their internal records.

(3) If by some chance AT&T is the stock, there are a number of useful
web sites that can guide you through the maze of splits and spinoffs
since 1984. If so, you might want to post a clarification.

(4) A free site, though limited in the companies represented, is here,
although it may not have enough years on record, depending on your
specific stock:

http://www.stocktaxbasis.com/sbstock.php

By the way, the IRS can't track your "purchases" except in an audit,
but the "sales" are reported by the broker on a 1099-B form, so they
will definitely be on the alert that you had sales. The default
position, which you won't like, is that your basis is "zero" and that
all the gains are taxable, so it's definitely worth it to spend a
little time tracking down those quotes (which assumes, of course, that
you have some record of the exact or approximate purchase date ... in
a pinch, you could work backwards from the certificate dates, if you
had them in physical form and have them written down or copied ... or
you could go back over your dividend dates to determine a "period"
when you acquired them).

If the shares were distributed to you from an employer plan, you might
have to value them as of the distribution date and allocate some
portion to ordinary income and some portion to capital gains...your
tax preparer could give you more information on that aspect of your
sales, if applicable. The IRS website also has publications that help
you work through that maze.