There are two RJ-45 ports on the back of the AE base station. Your cable modem should be plugged into the one on the left (looking at the back of the unit), and the computer should be plugged into the one on the right. Next, you need to make sure your PC is configured to obtain an automatic IP address. Since you didn't mention what OS you're running on it, I can only give you general instructions on how to do that. You'll need to find the network properties and look at the TCP/IP settings. Somewhere in there you'll find a checkbox that says "Obtain IP Address Automatically;" if it isn't checked already, check it. Next, restart the computer. (If you haven't restarted your PC since you tried plugging it in to the AE base, you may find that that's all yo need to do.)
I'm just having it sink in that you're using cable. You may need to call your provider and give them the AE's hardware address to get the cable modem to allow it to connect. The hardware address is a group of six pairs of hexadecimal digits like this: A1-B2-C3-E4-F5-00, and is found on the AE's label.