Professor agreed for a Skype meeting and then didn't follow up. Also hasn't responded to a reminder I sent a week after. Should I move on?
These things could happen due to a million reasons. 

My advice, 

Don't wait for other people, until you get a signed contract keep looking for other opportunities. This doesn't mean give this up, but it means that you shouldn't stop searching for other things. 

There are too many reasons why this might be happening to list them all (ie he's ill, family commitments, travelling, etc.). 

If he didn't agree on the Skype call, then technically, he hasn't left you standing. 

I suggest trying to get a contact number and calling. Professors get bombard with e-mails daily and it's easy for some to get through the net. If you call and he answers, an easy way to start talking is saying something along the lines of "Hey, I'm just checking everything is OK" or "Hey, could we set a type for that Skype call". 

Good luck.