Can I connect my PC to my cable modem wirelessly without using a router and just an access point?

Cable modems are usually bridges that connect a cable drop from your provider's network to a single IP-addressable device. For example, a cable modem can be connected to one PC by either USB or Ethernet. Or a cable modem can be connected by Ethernet to the "WAN port" on a broadband router. In both cases, there is one device with an IP address: the attached PC or the broadband router.

Broadband routers use Network Address Translation (NAT) to let multiple hosts share that one IP address assigned...

to the router's "WAN port." This is a typical configuration for wireless home networks, and is usually the easiest and most cost effective option.

However, some cable modems do support multiple IP-addressable devices. If your modem and cable provider both support this feature, you might be able to connect your AP directly to your cable modem's Ethernet port. Any station connected to your AP would become a separately addressed host, getting its IP address from your provider's DHCP server. Providers that support multiple IP addresses per cable drop usually charge extra for each IP address. For example, my cable provider charges $5 per month for leasing a second IP address. You would need at least three IP addresses: one for your wireless AP, one for your existing PC, and one for your wireless card. Caveat: I have never tried this configuration myself, but I think it's conceptually possible, given a cooperative cable modem and cable provider.