Some insert lamps are on all the time and some are never on (they are not broken). When I look at the lamp driver board, the transistors in question even look broken (see image).

Is it as simple as this? I replace every transistor where there is a problem.

Should I measure the transistors first, and if so, do I check the resistance or use the diode test? Is it ok to do it while the board is still connected?

Could other components be broken? Can there be another underlying problem? How can so many transistors be broken at the same time?

Thanks!

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Thanks for all the advice!

The machine was in this condition when I bought it and I don't know its history.

I have ordered components and will do the replacements and cleaning in a few days.

There is a new battery in place (see image below). Is this a type that can leak in the future? Are there any other, safer solutions?

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I have replaced the transistors and now the lamps work as they should. I haven't replaced or moved the battery yet.

Thanks for all the advice!