The hd that must have come from the computer that went caput (its capacity is 500GB, also a Seagate) does no dedoink when the button is pressed but ticks 4 times then misses a beat then 4 more - like an old gramophone record gone wrong.
Oh dear - not good news [ as you have probably gathered ]
The ticking noise is made by the moving arm [ that holds the read/write head ] bouncing back to the stop.
It is known as the "click of death"
Your hard drive is dead I am afraid. The head cannot read any data from the drive.
The other two drives seem to be ok.
You can treat the enclosure as a memory stick and search it in the usual way.
Any photos etc that you find can be transferred to the actual hard drive in the computer.
Once you have everything off the external hard drive that you want you can format it and use it for additional storeage / backup.
If you do format it - you will lose ALL data on the drive.
Let me know if you need any more help.
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but warns that it needs a scan. I do not know how to do that in W10.
Put the hard drive into the enclosure and connect up.
Click on the Files icon [ bottom of screen ]
Your external hard drive should be showing as a letter [ :E or :F possibly ] [ C: is your main hard drive ]
Right click on the drive letter of the external drive
you will see something like this...
Your anti-virus should show here.
Mine says "Scan with ESET internet security"
Click on it and follow the onscreen instructions.
It may take a while if you have a big drive.