The Volvo V70 uses a standard ignition switch and cylinder assembly. When the ignition switch fails, you will be able to turn the key but the car won't start. You won't hear any clicking sound indicating that the switch is activating. As long as the battery is charged and the other electrical components (starter and starter solenoid) are functional, you can assume that the switch is dead, and that you'll need to replace it.
Disconnect the battery. Put the key into the ignition and turn the ignition to the "run" position. This will unlock the ignition.
Slide the pinch pin into the access hole underneath the ignition lock and switch assembly.
Push up on the pin while you remove the switch along with the key. Then pull the punch out of the access hole.
Push the new cylinder and switch assembly into the steering column with the ignition key in the "run" position. Then, turn the key to the "off" position and remove the key.
Reconnect the battery.