Are you sure that the mpem is bad? Even a used one is expensive. While it doesn't necessarily mean the mpem is good, two beeps is a very good sign that it is working.
It sounds to me that you have two separate problems which might not be related to the mpem. If you haven't done it already, I would have the battery load tested. Most auto parts stores will do it for free. Also check for bad grounds, bad battery cables (if they "crunch" they're probably bad), and corrosion on the cables and connections. Since you probably ride on the ocean, check especially the three cables that plug into the mpem, clean and apply dielectric grease.
There's other stuff we can check, but check this stuff out first.
Lou