FYI I've opened a ticket with LS Support
The ticket with LS Support will not get you anywhere, because they will only give you support for paid products (e.g. Limesurvey Pro hosting or the Comfort Update). As your installations are on your own server and this does not relate to Comfort Update in anyway, they most probably will direct you to the forum.
Now, with the problem description it is fairly hard to help. It does not seem to be a general problem, because we would have a lot more complaints here. So it must be something specific to your environment.
Now, given that it happens on two different servers with different setups (Windows vs Linux) it doesn't seem to necessarily be something server related. Though it could be due to the same PHP settings.
Is this with the same survey or are these different surveys?
What is strange is that there are different errors. Might be actually two different problems.
What is the session setting in PHP?
Is there any redirect or email notification upon submit?
What I find strange is that this happens in two totally different Versions, both in 3.x and 4.x. This makes me suspicious that it has nothing to do with Limesurvey itself, but rather with your setup, or your network.
This servers are setup where? In your offices (if so, are they accessible only via LAN or via the web as well)? In a data center?