Use SharePoint Designer to temporarily rename the default.aspx file in
the root and create a small replacement page.

I found it easier to create a new, non-SharePoint, web site in IIS
Manager with the same IP/Port/Host Header. Then, still in IIS Manager,
stop the SharePoint site and start this new one.

I would add a second non-SharePoint IIS Web Site with a host header that
nearly matches your SharePoint site with a simple default  "under
construction/maintenance" HTML page in the root. When you go to do
maintenance, simply redirect all traffic from the SharePoint site to the
non-SharePoint site by changing the host headers on the IIS Web Sites
(or even better by changing a firewall, ISA, or proxy server rule). When
people attempt to go anywhere in the site including deep down links you
can configure IIS to just show the "under construction/maintenance" HTML
home page.

In short, while under maintenance, redirect traffic to a non-SharePoint
site. What's great is that this site can have host headers for all
site's that could be offline. There could be a dozen sites all under
maintenance simultaneously all pointed to the "under maintenance" site.

maybe I'm doing something wrong here. I need something that
will work while SQL Server is stopped (while we do the upgrade). So
on our staging server I did exactly as you suggested. In SPD I
replace our default.aspx with one that just displays some html. Then
I stopped SQL server, ran IIS Reset, and now when I try to hit the
site I get "Internet Explorer Cannot Display the Webpage".

The solution that you attempted (using SPD) is still using SharePoint, which of
course uses SQL Server.

Sorry, I should read better. I missed the spot where they were
upgrading to SQL 2005.

If you are going to be stopping the SQL server as well then what I
mentioned won't work. Your best bet then is to do what Paul Schaeflien
suggested. Stop the SharePoint webapp in IIS. Create a reqular IIS
website using the same IP, Portnumber and HostHeader as the SharePoint
site. Put the simple default.aspx in the new website. When you want to
go back to SharePoint, stop the IIS temporary website you created and
restart the SharePoint web app.