Linux crash or hang

We had several cases of Linux servers acting very weirdly, to a great variation of symptoms. As long as any of them are not explained, I expect them to be related, and the cause is suspected to be the virtual software provider, which in our case is : ESX VMWare.

We have some physical servers as well, which run the same Oracle Oracle software, and they have no issue at all. But that is just one of the symptoms.

Now, the cases vary, but this is one case:

I want to putty to a server, and Putty fails. But, instead of stating the server is unavailable, the cursor just hangs (before you enter the user/password). This is typical for a hanging server. So, it's up, but you can't contact to it in a normal way.