Sounds like the HD is shorted. If a short circuit is detected by the power supply it fails safe.
You can check the HD with a multimeter on lowest Ohms setting.
Pins 2-3  will show a short (zero reading).
1-2, 3-4, and 1-4 will be none zero (ie: > 200ohms) usually out of range (1) displayed. If you get zero then a definite short.
If above readings okay, connect power cable from test computer, but don't connect data cable to HD, power on, if system boots then the problem is likely in the controller card. You can swap a contoller card from same model if available then retrive data.
If it's dead, and your mechanically inclined, and the data recovery is worth it, and you have a working model available, then disassemble and put the platters in the working one.
Also worth mentioning is an oddity I've come across a few times, HD's that wouldn't work when jumpers were set for master or slave, yet worked fine when jumpered for cable select. The jumper setting were checked, rechecked, verified with specs, used different test computers, but that was the only way they could be reclaimed.
If you do get it going, run a virus scan on it before recovering files.