This is mostly a set of notes to myself and to guide friends in sorting out network problems. If it helps you too, great.
Most of this is strictly about network and DSL/cable internet access; it pretty much ignores dialup.
Start before you have problems
When you add a new device to the network, observe how it behaves when you turn it on and how it acts when it's working right. Knowing what it's supposed to act like can help you isolate the bits that aren't acting right later and ignore the ones that are.
Draw a simple diagram of your network, its devices and connections. Note any special information about each, such as the brands/models of network cards, special hardware configurations, IP addresses and anything else you learn about when you install the device.
Consider keeping a log for your notes. In it, record dates and particulars when you install new hardware or software.
Buy a spare network cable or two. Short ones are cheap and can be handy for testing. A spare in the longest length you normally use (or even the next longer one) is good to have handy as well. Don't assume that new cables are OK; test them. Be sure.
Don't buy cheap network components and cable. The savings disappears when your network stops working, and you end up in the red when you have to replace the stuff with something decent in the end. Save money and time by buying the good stuff to begin with.
Shut down and restart everything
Quit Windows and power down the PC.
Turn off everything attached to the PC.
Turn off all external network devices (hubs, routers, modems, ADSL/cable gadgets, the works.
Now leave it all off for five or ten minutes while you get a cup of coffee and mull over what software or hardware changes might have befallen the system between the last time everything was working right and now. Take notes. There may be a quiz later.
Starting with the devices closest to "the outside" and working back toward your PC, turn everything back on one device at a time.
Let each device go through whatever little initialization dances it normally does before going on to the next device. Watch carefully for discrepancies between what it does now and what it ordinarily does. Take notes.
For example, you might first turn on your ADSL/cable box, then any routers or hubs, then the peripherals attached to the PC (printers, scanners and such) and finally the PC itself.
Check for physical connections and LINK
Most network devices have a (usually green, usually labeled "LINK") LED that indicates a physical network connection.
As each device comes up and again after everything's on, make sure that the LINK lit is lit on every device that has one. The light may blink on and off when there's network activity - that's ok - but if it's off altogether, that points to a problem.
If there's no LINK
Swap cables; try your spare good one. Or swap cables with a computer that's able to connect. Swap cables with any other device on the network. If the problem "follows" the cable, throw the cable out, replace it with a good one and you're probably done.