Getting files off old Mac clone without keyboard, mouse, or monitor
The best course of action is to pull the data off the drive via USB with a USB to SCSI adapter like the Adaptec USBXchange.

You can do this without spending a lot of money (definitely less than having a shop or a tech do this).  Though the hardware is obsolete, you are in luck because macOS (OS X) supports USB Attached SCSI meaning your drive will show up as a mounted volume.

To do this, you will need the following


Adaptec USBXchange USB to SCSI Adapter.  This will give you the USB attached SCSI functionality.
HD50 to IDC 50 (External/Internal) SCSI Adapter (removed from bracket if possible).  This will convert the IDC 50 pin connector on the HDD to the HD50 pin connector (for external SCSI drives) on the USB adapter.




Probably the most daunting task is getting access to the drive, but in actuality, it isn't all that difficult.  The PowerCenter 150 is a Mac clone and is put together more like a PC than a Mac in that respect.  Opening the case and accessing the drive is no different than the procedure for opening a PC case.  Basically, a few phillips screws on the back hold the side panels on and after removing them, the panels will slide off giving you access to the internals.



Procedure


Remove the hard disk mounting screws (yellow circle; both sides) so you can access the drive
Remove the grey cable from the main board; leave the power cable (red circle) attached
Connect the grey cable to the 50 pin IDC port (square) and the USB Adapter to the HD50 port (port in the shape of an elongated "D")
Connect USB adapter to MacBook Air, and power on the PowerCenter computer


The drive should appear on your MBA and you should be able to pull of your data.