How can I send a signal to a home server when the doorbell is pressed?
Doorbells generally run on 16-20 volts AC power.
You can detect events using a microcontroller as seen here:

https://electronics.stackexchange.com/questions/96136/how-to-sense-24v-ac-thermostat-with-a-5v-microcontroller

Some computers (Intel Edison, Raspberry Pi) both run linux and have GPIO inputs; otherwise you'll have to rig up a microcontroller and attach it to a home automation pc.