How does your ISP assign you an IP address? Is it a "static" address, or do you obatin your IP address automatically (like, via DHCP)?
Have you ever connected to the Internet with your PC directly connnected to the cable modem? If so, could you do it again? If you could do that, once your are connected to the Internet, bring up a "command" window (In XP it's Start-->Run--cmd In W98 it's Start-->Run-->command). In the command window enter the following command:
ipconfig/all | more
The character between "all" and "more" is the "vertical bar" key (Shift \). That will keep the info from scrolling off the screen. Just hit the space bar to on to other screenfuls.
That will tell you how every network device on your PC is configured. If your PC obtained your IP address automatically the fields "Lease obtained" and "Lease expires" will have date/time info in them. If your IP address is a static one, those fields will be blank.
Also, what is the IP address of the AP? You say you reset the AP. If you did, then it will have its default address. You should be able to look up what that is in the documentation.
For example, let's say the default IP address of the AP is 192.168.1.1. That means that the subnet mask is almost certainly 255.255.255.0 If that's the case, then your PC's IP address must be 192.168.1.x, "x" being some number between 1 and 254 (but not "1" of course). It must be in the same subnet as the AP (that being 192.168.1). If the IP address is not in the same subnet as the AP, your PC will not find the AP.
However, I suspect that the AP you have will not work to get you out onto the Internet. Here's why I think that. Let's say that your ISP has assigned you an IP address of 172.16.10.115 with a subnet mask of 255.255.255.0. Then, your AP would need to have an address of 172.16.10.x. But, what should "x" be? Anything from 1 to 254? How about "115" (since, in this example, that's what the ISP assigned you)? But, then what should the IP address of your PC be? Would need to be 172.16.10.x (must be in the same subnet), but "x" can't be "115" because that's what you assigned to your AP. So, how about "116"? Well, that's the kicker. "116" might have been assigned to another one of your ISP's customers. You can see the problem with any of the other numbers from 1 thru 254.
Most likely you'll need a "wired/wireless router>>>WAP" as another poster suggested. With a device like that one "side" of the router would have the static IP address your ISP assigned you (or you obtained automatically via DHCP), and the other "side" of the router would have an address like 192.168.1.1 (and your PC would have an address like 192.168.1.101). The router runs a function called "NAT" (Network Address Translation). The router takes your "local address" (like 192.168.1.101) and "translates" (I'm obviously leaving out many details here) it into the IP address your ISP gave you. When something comes back to you from the Internet, your router translates the address back to your local address.
Now, you might think all of this stuff sounds dreadful and hopeless. Not to worry. I configured a "wired/wireless router>>>WAP" last night in a class I'm taking. I had never seen one or laid hands on one prior to that. In about an hour and a half I had 4 PCs going out onto the Internet through it.