The DNS stored by computer means it keeps a little record of which server it needs to request information from for your
website hosting i.e. which
website hosting your server is hosted on. Now, if you change servers and the DNS is still the old one, your computer will look at the old server address, not the new one and you will keep seeing whatever is on the old server. The DNS on your computer will update within a few hours automatically however you can flush it and make it refresh. This means you can see what's actually going on now.
To do this, open command prompt in Start, Programs, Accessories and then in it, type ipconfig/flushdns. It will then get the up to date records from your ISP (providing they have update their servers etc - this is why it can take a while to propogate).
I would email/get in touch with support and say you've had the domain transfers confirmed, why can't you change them on your members account panel? Also enquire about the renewal. It may be if you renewed it after the transfer had been initiated, it hasn't registered on the system. This would be something you need to check with whoever you got to renew them as it could have been affected by the transfer.