Page Cannot Be Displayed Errors

We're running Windows Server 2003 Web Edition for our web server. We've got
about 10 web sites on it, only one of which is very active (meaning that we
may have 25 or 30 hits going on at any one time, if you can call that busy).
Periodically, people get "Page Cannot Be Displayed" errors (It says DNS or
Server error at the bottom). This is an IE error message. FireFox says
"Time Out". The strange thing is that a split second later, you can press
your F5 Key to refresh the page, and it pops right in there. So, this isn't
something that is happening all of the time, only some of the time. This is
not happening to any one individual. It happens to me frequently (in
Florida), to people in Ohio, Kentucky, Virginia, and several other states.
This is not a problem "on the other end". It has to be on our end some way.

Hardware:
* Dell PowerEdge 1650
* Windows Server 2003 Web Edition OS
* Road Runner Level 2 Business Class cable modem Internet connection.
* Originally, had a D-Link DI-604 router, and an 8 port network switch, but
we've swapped that temporarily for an 8 port NetGear router, and removed the
D-Link and 8 port network switch.
* We have another server acting as a Domain Controller, and also hosts our
SQL Server. This machine is pretty new, has lots of memory and plenty of
CPU power.

Software:
* The Web Server is running as a Web Server (IIS), FTP Server, and Mail
Server. FTP Server is really not all that active, and the Mail Server
fluctuates. It's mostly just a few hits once in a while, unless someone
decides to send out a mass e-mail, in which case it does drag down a bit,
but you can really tell when that's happening.

Following is what we have tried so far:
* We have called Road Runner several times. They've been out and checked the
lines, checked the modem, replaced the modem twice (I believe). They have
done some extensive testing, and they tell us that their part of the deal is
clean.

* We have had a network technician in and he has checked out the network on
our side, doing lots of testing, and he tells us that our network is clean
on our side.

* We have replaced the original router/switch with a different
router/switch.

* I have been checking the IIS logs, and what I believe I'm seeing is that
when this error occurs, there is no entry in the IIS log as to a page being
sent to the requestor. That tells me that one of two things is happening.
Either 1) the request isn't getting to IIS, or 2) The request is getting
there, and IIS isn't able to respond, therefore it doesn't log the response
in the logs.

* I've checked the Windows Event logs, and there is nothing in there with
regard to this problem.

* I have also done some testing with WFetch, and I periodically get an error
when I'm testing remotely, but when I test with localhost directly on the
web server, I've never seen it fail, and it returns pretty quickly.

What I think needs to happen is that we need to be able to track a request
from the time it comes in through the cable modem all the way through when
IIS responds. I'm aware of how to do some of this, but I'm not aware of how
to do all of it. Plus, I am no network technician, so when I'm looking at
the results, I really don't know how to read some of this.

If anyone's got any ideas at all on this, we really appreciate you chiming
in. We're desperate to resolve this problem, because it may be costing us
business as people cannot connect, and become dissatisfied with our service.

Thanks,
Jesse