Volvo wont crank

Ok - we can only offer possible causes here online (of course) .. Some automobile repair skills will be required for testing / diagnosis ... The small wire going to the starter solenoid is prone to corrosion - suggest removing that wire and TEST for battery power while helper HOLDS key to start position using a 12 volt test light. Now - as you stated - Jumping across the solenoid terminals makes the starter engage by simply putting the required battery power on that wire - therefore we know there is either no power coming from ignition starter switch - OR - the wire is not making connection at the starter solenoid - that is the first step in the resolving this issue. Good luck!