A week ago, I contacted a professor regarding a PhD position in his group. He replied by saying that he is in search for a PhD student and after examining my CV, he said that he would like to organize a meeting over Skype and also asked for my transcripts. Therefore, I suggested him a date and time for the meeting and also sent him the official academic transcripts but he hasn't responded since then. I had also sent him a gentle reminder a week after my last correspondence. Still no reply from his side. How should I interpret this? Should I move on?
These things could happen due to a million reasons.
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".
Happens all the time. "We should set up a time" is not the same as "Set a time". Nor is it polite for you to dictate time; his schedule is busier and more complex than yours--and even if not, you are the one asking for a 'favor'. If possible, get ahold of the admin assistant, whose job it is to deal with such things, and have her/him bother the professor.
I don't have enough reputation to comment on Mox's "answer". So I'll write it here.
He's right, you can't assume someone agree's to a time without them actually agreeing to it.
He's also wrong, he assumes your timetable and that of the professors. Also assuming there are assistants to deal with these issues, again pointless.
This problem (missed contact) is one that happens throughout life and you need to understand people aren't against you, it's just sometimes we mix things up and/or forget to reply to messages. I strongly suggest always giving benefit of doubt and try a different approach. If you don't get a reply, try a phone call, if you can't get through, try knocking on the door.