Hello Mark,
What is the model of the 4GB memory module? Additionally what CPU is in the system?
According to the beep codes, you may have a pairty issue. Without further information, I recommend installing a single stick in the first slot, turning the computer on, and leaving it alone for a few minutes, if it starts beeping with the single stick record and relay that information.
Lastly will the machine boot if you install the single 4GB memory module?