I am by trade a PC engineer, but now I only work free-lance, as working within a company limits my options and time for an individual job.
Now I call myself a "Holistic Computer Doctor" as I fix the owner as much as I fix the PC.
Long-term this makes my job easier, as a more educated customer can ask me a clear and concise question, and I can give clear and concise help (especially over the phone).
There are a few options regarding getting your PC online.
WiFi and Ethernet
get the newest most complete version of your network card drivers (Updated motherboard drivers are also a very
good idea), by using another PC.
use hard-wired ethernet connection if you can. It is faster and more secure.
3) Try a different ethernet cable. Some cables are for PC to PC, some are for PC to router
4) If your WiFi is not connecting to the net, but is connecting to the router, try temporarily disabling the encryption on the router.
If you are using "Windows Zero Config", try connecting with any software installed with the updated drivers (sometimes an optional download).
5) Try moving the PC and router to the same room to see if it is a reliability, signal quality issue. (signal strength and quality are very different!) If you are lucky, the manufactures software that comes with the drivers will also show you the signal quality.
6) Reset the router to factory defaults and try again.
7) If someone has incorrectly used some tweaking software, or switched off certain network sevices, this may be the problem.
Your manufacturers support page for your PC will have a list of the chipsets and cards.
If it is home-made or a re-build, the free software "PCWizard" will tell you everything you need to know.http://www.cpuid.com/softwares/pc-wizard.html
I'm sure a few others have some useful insight into getting your connection going. I have just covered the basics.
Hope it helps