Berea, OH
Do you have a DMM or voltemeter and know how to use it? Check the solenoids for DC voltage. With as many solenoids are out, there could be a wire broken (power side of solenoids are daisy chained to a single source) The picture shows burned general illumination (GI) connectors. These will need to be replaced and repinned.
Before you do any of that, I would recommend you read the basic introductory pinball repair information at the following links:
http://techniek.flipperwinkel.nl/desega/index1.htm
http://pinwiki.com/wiki/index.php?title=Data_East/Sega
http://www.pinrepair.com/connect/
