I then use the CD supplied with the printer to install the driver and select the printer on the network using the Brother printer. This seems to work at first; I can print the initial test page just fine. However, when I send print jobs, the queue says "cannot connect, access is denied."
I had about given up entirely. I finally solved the problem by getting on the Windows 7 machine and installing the LPD Print Service component. Then, I went to my Vista computer and installed the LPR Port Monitor component. After that, I was able to install the printer successfully. I chose Local Printer, created a new LPR port, and entered the address of the Win7 system, and entered the share name of the printer.
It appears that the problem is caused by a mix of permissions changes to the Win7 spooler folder perhaps caused by an update, the Brother driver itself, and the mix of 32- and 64-bit systems.