@Dell960User 

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Nothing special just standard 5.25 inch or 3.5 inch floppy.

Optiplex 960_service manual 

You need a cable

Standard Floppy Drive cable

and the drive

SONY Floppy Drive 3.5 inch

There are usually 3 screws for the drive inside the case attached to the front bezel filler panel. 2 go onto the drive where you can see and one goes on the back side where you cannot see. They are shoulder screws and lock in place.

The 360/760/960 and 380/780/980 are the same so this is probably better for how it goes in.

optiplex_780_Service Manual

Re: Does anyone have information on the motherboard connector for either the MT or SFF

960MT mobo uses standard 34 pin FDD connector (white).

960SFF mobo uses a mini 34 pin FDD connector (black) and uses a thin ribbon cable E41447-HWCS.

960MT uses standard 3.5" form factor FDD.

960SFF uses slim line FDD such as Sony MPF820 Slimline 1.44 Floppy Disk Drive Dell 8C043

The flexible cable for slim FDD in 960SFF has 26 pins on the motherboard connector side.  it is a single row of 26 pins.

the other side of the cable connecting to FDD has a flat ribbon connector demonstrated in this video. Tutorial on How to properly connect the Flat Ribbon Cable to a 26 PIN 1.44MB Floppy Drive Emulator - YouTube

Does that proprietary cable have 26 conductors on one side and then 12 conductors on the other side (3 top, 6 middle, 3 bottom)? 

Ah, very nice! Thanks so much for your help. I’ve been searching all over for a floppy drive for this computer and none of the references are for the 960 SFF. This clears things up for me!

It is the same slim FDD Dell uses in 755 and 745 SFF.  DP/N GJ309.

The ribbon cable 26 pin connector on motherboard side has a plastic tab key so it can only be inserted one way into the motherboard socket. 

@Dell960User 

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A better also supported option would be a USB Floppy Drive. Which can be used with All Dell models Desktop or Laptop regardless of size and does not require removing anything or finding propriteary parts.

MPF82E 08K9835

External USB Floppy Drive

@Dell960User 

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Standard FDD connector contains 34-pins not 38.

(Shugart interface)

34-pin for 5.25 / 3.5 diskette drives

The Dell flex circuit connection is proprietary not standard.

Every other pin is ground so 17 pins are signal and 17 pins are ground.

In this case, I was to suggest the same thing as speedstep.  That way, @Dell960User, you're not going through as much trouble for floppy disks, which are somewhat unreliable.

Years ago, before I had internet at home, before I had flash drives, I'd use floppy drive to go between library computers and mine.  Sometimes it would be hit & miss if the floppy still had the saved info/data/file once I got to the destination.  Not any one of my floppies retained anything after some years just by sitting in their case.