The schematic for this game is not available. Folks have been searching for the board schematic and none has been found.

Firstly, disconnect the power wires -- red ones from the burned coils. Although the driver transistor maybe blown, no use taking a chance that the burned coils might be pulling down some voltage or causing some problems. Insulate the removed connectors so they don't short against something.

The problem you are working is hopefully associated with either a strobe or return line. If you can determine which switches are causing you the problem, and they are either associated with a specific strobe or return then you can follow the path to a device that may be the problem.

If your meter has a frequency counter setting, perhaps you can check the strobe lines for matching frequency.

As there is no schematic for the pc board that is the likely the reason there are no responses to your
posting.

Give it 24 hours and someone may have some information regarding the PC devices associated with the switch matrix.

http://www.arcade-museum.com/manuals-pinball/A/Aspen%20switch%20matrix.pdf