Compression test might be good information to know at some point, but I would think that you would hear it trying to fire-off. Even if several cylinders had poor compression it would get somethin poppin off. Would not be pretty, but you would still have something happening.
If compression were a factor, it would kind of start. You might notice blow-by. Or... in an extreme case of blown rings, maybe even raw fuel in your oil pan.
Not sure I would fixate on compression testing in trying to diagnose your particular issue. But I could be wrong. That is just my thinking.