I have a netgear wireless router connected to my cable modem and my
main PC.  My second PC has a netgear PCI wireless card installed.  I
can connect my second PC to the router, but I cannot access the
internet.  If I plug my second PC directly into the cable modem I can
access the internet, but when I reset everything and access the router
with the second PC, once again I cannot access the internet.  Please
help if possible.

Get the latest drivers, backup all your work, make sure you can change
the settings in your router,and restore them.
1-Acess the router with a PC with cable phisically connected to the router,
2-Remove all security from the router (WEP)
3-check if router has ip addresses assingned to allow connection to
router if yes remove them
4-check if router has mac adresses assign to allow to connect to the
router and remove them
5-save changes to router
6-set the router to DHCP and bradcast SSID.
7-go to the PCs, and under network connections make sure in properties
internet protocol tcp/ip is set to obtain everithing automaticaly
8-turn off all firewalls and set windows to define your wireless connection.
9-Shut down everything
10-then by this order start, Cable modem, router, PCs.(check for fire
wall should be off). if you get internet on both Pcs start from there
to where the problem is, start firewall...

Please notice if you set wep password it can be used ascii characters
or hexadecimal and if you use windows to control your wireless it is
best if you use hexadecimal number and letters without the ":"
hope this helps.I had the same problem :) but with different router.