Oh! I figured disabling the service would have stopped it.
I'm using a Linksys Wireless G router, but no ports have been manually opened. But if you say I don't want to close it, then I won't mess with it. The alerts are just more of an annoyance than anything else.
I used 'Remote Port 135 Test' in DCOMbobulator (
http://www.grc.com/freeware/dcom.htm), which shows the port is open to the public internet. Oddly, I have another PC that I work on simulatneously throughout the day... same operating system, identical setup in terms of firewall and ant-virus. The other computer does not receive these warnings. I also tried the DCOMBobulator remote port test on that PC, and it indicates that port 135 is closed.
Thanks for pointing me to ShieldsUp. I'll give that a shot and post back.
Edit: I should have mentioned earlier that on the PC experiencing this trouble, I use a private VPN service. I've used this service for about 5 months now with no problems though, but might have something to do with the issue here.