Electronic Alarms and Home Security Devices - Can My Door Bell be in my alarm?

I got a home I have lived in for about five years. This home has an alarm system that has never worked but also my door bell has never worked/ I have been buying those cheapy built wireless remote doorbells but they only seem to last about six months. I have decided to try and fix my doorbell but I cannot find it anywhere. On my front porch, I have a lot of wires that used to hook up to the original "switch", but cannot find anywhere in the house an actual ringer or a transformer in the attic. My house is two story so it's going to be hard getting anything new wired in..... but I am ready to tackle anything. Can the original doorbell be in the alarm system that is inoperable? Any ideas?

Not at all likely.

A normal door bell system will have a small AC transformer, usually hardwired into the house electrical (if not in an attic, near the breaker panel), the buttons and the sounder unit. If you aren't even finding the sounder unit, the odds are that someone removed it and spackled over the holes. In a two story house, doorbell sounders are typically in the vicinity of the stairs so that it can be heard on both floors.

Sadly there is no standard. You have a bit of a snipe hunt to find the original location and hardware.