Hi
the issue has been sorted.
I can say it was something simple, but it wasn't as it was a compatibility issue between ESXi and Vcenter Server. It took many days until I realised about it.
I re-installed in the end ESXi 5.0.0 (and NOT 5.1.0 as it was originally done) while Vcenter Server was also 5.0.0. The communication between both parties happened without a single issue.
When I got the license for ESXi 5.X.X, I downloaded the latest versions never crossing my mind compatibity issues should happened as anything was about the same Release level.
That was a wrong assumption.
This is a common mistake by many software companies which misslead customers. So priority before installations, compatibility tables (if any!!!), or just test until it works then after you can start migrating and installing VMs (one of the got corrupted during the tests and was fun to put everything right again)
Many thanks to all those who came around with suggestions.