I’d at least get a plumber to check it out. You could snake it yourself probably but you could also make it worse. If the pipe’s broken, you might as well just get more debris falling into it and clogging it further.

A regular plumber visit/check usually isn’t that expensive. Not cheap but far from 20k expensive.

It could also be connected to your flooding too, so you probably actually want to at least evaluate the damage ASAP. If the pipe’s broken, you just have a convenient pipe to drain all the rain water straight to your basement.