/// Luke, The Volvo starter won't run on less than 8 volts. It doesn't matter if the low voltage is because of the battery or battery cables. Try using your jumper cables to bypass the negative battery cable. Test the voltage drop from the battery to the starter solonoid bolt while trying to crank for the postitive cable. Electric motors do wear and it may be the starter but I too would bet on cables. As an emergency measure you could replace the battery cable end.

NAPA sells a heavy compression cable repair end that adds about six inches to the cable. I have posted the details several times. It is the best repair I have found for this problem

WET START PROBLEMS ... Check the plug and high voltage wiring by watching the wires in total darkness. If the plug wires arc replace them. (car running of course) It sounds like you have a plug wire problem when it is damp. Some Volvo plug wires have resistors in the ceramic end elements. There is a resistor in the rotor and a carbon contact in the Bosch distributor caps. These also cause trouble.