If you have checked, and the pins are straight, another common problem with these chinon drives is, that the little detector switches gunk up over the years and start misbehaving.
There are three such switches in a HD drive and two in a DD drive.
They can be opened up and cleaned, but you must be very careful when separating it, as there are small bits of metal + a spring inside.
The reason it spins the disk randomly is, that the disk detection pin is making intermittent contact. It is the one that is behind the write protect detector when you look in through the front opening of the drive.
I don't really have any advice on how to proceed with cleaning them - open it up, clean it, reassemble. However the parts are really small and spring loaded, and you need good nerves.. :-)