Ouch. That ping noise doesn't sound too healty..

Anyway, perhaps the old drive is unable to find the "beginning" of the disk.
I had this issue quite a few times. It also happened even though I was using the park program..

(By the way, not all parking programs were the same. Some were made for a speciic fixed disk model,
ie, they were hard-coded to land the r/w heads on a specific cylinder. Universal programs were available, too.
I believe Central Point's PC-Tools included one, as well.)

In case my MFM drive got "stuck" in the process of finding its starting track,
it sometimes helped to switch off power at the moment it did a seek.

When I quickly switched it on again, it successfully finished the re-positioning.
Anyway, this is a dangerous method. It could also hurt the power supply.

^ Sounds like one of the heads in the drive is bad, that's why you get that repeated 'pinging' sound. The drive's processor is trying to get a track ID from that head and failing, and in so doing it rezeros the headstack against the crash stop before retrying, which is what makes that repeating ping noise. Judging by the really rough spin up spindle sound, I'd wager that's the least of this drive's problems.

Depending on which head it is, there's a very small chance you could just format the drive minus that head, and accept a loss of capacity, but I wouldn't put a lot of money on it. For example, if it's the very last logical head that's bad (and it's not the servo head), then you might be able to just format it with the head count reduced by 1. If it's any other head, I'm not so sure what you could do.