I have got my airdroid working. However I do have an issue (more on this later).
I looked at the discussion in
http://forum.airdroid.com/discussion/9367/airdroid-2-can039t-connect-over-mobile-data#Item_45 and realised that the issues may be similar. I cleared the airdroid cache on my phone and switched off wifi and restarted airdroid. Chrome web.airdroid.com connected successfully. (at no stage did I clear Chrome cache)
To get wifi working, I had to restart airdroid on the phone and again, no issues. This was on the same network.
When I'm at work, I have my phone connected to wifi on one network, and my pc connected to lan on another, and this is probably why I couldn't get access. But the issue persisted when I tried mobile network.. so maybe the caching issue needs to be fixed.
The main issue I have, it would be great for web.airdroid.com, to try and access the mobile through wifi and upon failure, try the mobile data (with user choice of course). And this would be great without having to restart airdroid on the phone.
Hopefully this will help some people here. I still wish the devs said hello once in a while on this forum.