I hate to be Johnny Raincloud, but if your USB-to-RS232 adapter didn't come with a Windows 7 driver, there's a good chance it's not going to work with Windows 7.
After trying several cheap adapters that wouldn't work with Windows 7, I eventually bought a more expensive one from Radio Shack.
Like the others said, though, we need to know which adapter you're using to tell you for sure.