Issues transferring wordpress sites to new hosting

Hi,

We're in the process of transferring two company websites. One hasn't gone live yet and is in the care of our developer, and the other has been bought from another company.

Panoptic:
Despite having paid a developer to design the site, we're having a lot of grief trying to transfer it from his hosting to our own. He's tried to upload the backup to our hosting a couple of times now and every time he gets a running time error and the resources max out on our hosting.

GoDaddy have said that he shouldn't get a running time error if he's uploading through FTP and if he is getting errors then it's because his code is broken. However, the site currently works fine under his hosting where we built it.

We have limited knowledge of these kinds of transfers and none of us in the company have ever transferred a site ourselves. Any advice on what needs to be done or what needs to be considered here would be much appreciated.

Clear Comms:

The developer who designed Clear Comms has said that he can't advise us on how to upload our site to GoDaddy. He believes that GoDaddy would be the best people to ask. But having spoken with them yesterday, I don't believe they have any clue. The guy on the phone said that only our developer could tell us what to do. We don't have a developer for this site on our end.

We have the full ftp back up of the site which was given to us by the original developer. What we don't know is how to uploaded it? We have access to File Manager through GoDaddy but the FTP logins are not working for the wordpress we've set up in preparation on GoDaddy.

Please advise. We've been banging our heads against a wall for over a week with these transfers and gaining no ground.