Need help with flaky internet connect

[Moohasha]

I have cable internet through Charter (not for much longer though! Verizon is now available in my area with fiber optics!), and my connection has been pretty flaky for several months. I've called them out to do something about it, but I've lost faith in their service guys? Why? Well, the first time the guy came out, he gave me a hard time for moving the modem from where they installed it, criticized my wiring job (I moved several electronics into a hall closet and ran cables through the walls and attic), and then said I had cables going into a splitter in the attic and that was reducing my signal. A few weeks ago, another guy came out and said my problem was than I had cables going into a splitter in the attic and that was reducing my signal. Wait...didn't the first guy fix that?
Any way, I'm still having issues, and I'd like some advice for identifying whether the problem is my router, modem, or ISP before I go out and start buy/paying for new hardware/service. The router and modem are both fairly old (modem about 4 years, router 5 or 6). The problem is that the flaky connection is intermittent. It comes and goes. So I can't just plug directly into the modem and say "There, now it's working!"
A few more symptoms: whenever I can't connect, my network connection status in Windows doesn't show that there's anything wrong with the network, or my connection to the internet. However, reseting the modem and router usually fixes the problem.
So does anyone know a good way to test all three of these things individually to identify where the problem is? I'm probably going to switch to Verizon in the next month or two anyway, but I'd like to know if I'm going to keep having these problems after I switch because the gremlin is in my router or modem.

[jacmoe]

A good idea would be to ask the people providing your connection, if it's your ISP or your phone company, to monitor it for a day or two.
I had the same problem, but it turned out that it was a broken electrical cattle fence sending electricity directly into the cables a few kilometres away.
After they fixed the problem, the connection was good.
Make them monitor it to see if they can spot anything.
If they're not willing to monitor it for you, switch provider.
It can be the cable at fault.

[Moohasha]

Okay, at this point I think it's the router. The problem now ALWAYS occurs about 3-5 minutes after booting up. I can get online and open a website or two, and then I lose my connection. And by lose connection I mean I can't access anything online. I'm still connected to my network and can see my wife's computer and the router.
Going over and rebooting the router fixes it, and I don't have anymore issues until I turn on my computer again the next day. I would say maybe it's something with my OS (Windows 7), but it happens to my wife's computer to and she's running Ubuntu. So maybe my router is pooping out when some new device hooked up to it first boots up? Is that possible?

[jacmoe]

I had that error too before I realised that I needed two IP addresses more.
I have four dynamic IPs which gives me two connections.
Could be that.