I unplugged the fan and used a Rosewill 12" fan extension cable to run the rear case fan to the Sunbeam, and I also plugged my front case fan into it. I then plugged one of my PCP&C Silencer 610's IDE molex plugs to the power connector.
The problem came when I turned the computer on; a loud continuous whine came from the case. Also, when I pressed the On button on the front of the case the computer clicked on, but then went right back off and then turned on again. I made it to the desktop without any other issues. I could see my CPU fan was running and the front case fan, but the rear fan was not.
I turned the computer off, plugged the rear case fan back into the SYS_FAN1 header, left the molex IDE plugged into the multi-port along with the front case fan, and turned the computer back on. The computer booted immediately without making any noises and without doing that weird off/on thing, and the rear fan started running.
I'm stumped as to what happened. I'd like to have the rear case fan plugged into the multi-port as well as any other fans I might get so if anyone could give me some suggestions I would sure appreciate it.