My Book WD3200C037

I have a My Book WD3200C037.  It was working great on my old computer but then I had to get a new computer and now when I hook it to my laptop while the laptop is off, turn on my laptop, it pops up as new hardware recognized, states it is a My Book but when I click on My Computer the external drive isn’t there.  I have tried everything.  I am pretty desperate as I trusted this drive to about 2 years of family pictures that I just have to be able to recover.  Any advice?  Please please help me figure this out.

Look in Disk Management and see if the drive shows there and has a drive letter assigned.