The keypad is the whole system, hence the large number of wires on the back. All the power, telephone and zone loops are on that one harness. The 4130 is one of the original all-in-one systems. . . . and AIOs are not considered serious security. It's also about 20 years old, which is an eternity by alarm system standards.
A new AIO system will not be very suitable to you as they are meant to use wireless devices and only have one or two hardwire inputs; the 4130 has 9 hardwired zones. If you want to replace the system, get something like a V20P; it has tons of features and expandability and because it's Ademco, you already know how to operate it.
I would recommend mounting the control panel in a secure location and putting the keypad where the 4130 was (if you like the location). To get the door contacts/motions from the 4130 location to the 20P you have a couple options. The simplest - at least in concept - is to extend each of those wires to your 20P. Another option (one I've used a couple times) is to put a zone expander in the wall and run a keypad wire to the main panel. The 4130 usually requires a large hole to be cut in the wall, much larger than any modern keypad would cover. Since I'm not about to patch and paint drywall, I got a nice piece of wood (plaque from a trophy shop) to cover the hole and then mount the keypad to that. It is also easily removable if required to access/service the zone expander inside.