Hah - you can't really use old arcade gear as if it is a giant game console, firstly most of it is ten times older than it was ever intended to be, and secondly the games were designed to live bolted inside cabinets and be very rarely handled. Combine the age with the constant plugging/unplugging and handling and you end up with fairly unreliable hardware.
All I know about RP monitors is they are insanely expensive to repair (think thousand$ as opposed to hundred$), if it really is a monitor issue and not a PCB fault, and if it is not a simple issues you can resolve yourself eg loose connection, bad power supply, then it is almost certainly landfill.