Tinabanana - the first thing you need to do is get a schematic of your game. Follow this link for a schematic.
http://www.ipdb.org/search.pl?any=road+kings&search=Search+Database&searchtype=quick#1970
This will allow you to determine which transistor controls which solenoids. Look on the very first page and you will see that there is a table that shows the solenoid and which transistor controls it along with wire colors, connector identification, etc. etc.
Once you identify the transistor you can use your DMM to test it. Also, you can clip a wire to the tab of the transistor and then ground that wire. This should fire the transistor activating the corresponding coil.
Give this a try. Let us know how it goes. You can be sure you will get lots of help here. I have now repaired/restored four machines with the help of my fellow pinsiders! I am about to get started on my 5th machine in a couple of weeks. You will enjoy repairing your machine and get a great sense of accomplishment when it works and you did the repairs.
Al