You can go to almost any of the AV providers and get a "remote scan" for infections, and the better ones offer a more general "security scan" that will identify any improperly open ports you might have. Since I use Norton, I usually go there, and they have had a scan that well check whether you have a port open that presents a security risk. The ports that they confirm are open for a "normal" purpose generally aren't mentioned in the report that they give you, but the scan will tell you if you have one that shouldn't be open.

(Win2K had one port they didn't like, that couldn't be closed without trashing the machine, but most other recent Win versions should theoretically be capable of being "invisible" to unathorized outside intruders.)

I can't speak to the other providers who offer similar scans, but Norton may take you to a page to show you what they offer to "make everything beautiful" after the scan report is done; but they don't hassle you with any high pressure salesmanship.

I don't have a link handy, but it shouldn't be hard to find with either Norton or Symantec as a search term. Just make sure you go to their "real" site (or a real one for another AV maker of your choice) as "scareware" that tries to look like they'll do things for you (but end up doing things to you) are far too common.

John