I bought a new dryer while living in a new construction apartment. I then moved to an older home (pre-1996 construction) with a 3-prong receptacle. I was about to buy a 3-prong plug but decided to open the receptacle and take a look. In the box I was surprised to find 4 wires with the ground wire cut very short and not used. So, can I use the 4-wire, wire nut a longer ground, and wire this to a new 4-prong receptacle that I'll buy?
That would be fine, as long as you make sure that unused ground wire is in tact and properly terminated back at the panel.
Testing continuity to ground is not IMO a sufficient test, since a neutral and a ground would both show continuity to ground. Hopefully the cable is run exposed where you can see it and verify that it goes where it should in the panel.