Connection problems with SQL Server in ASP.NET applications using out-of-process session state

I have several ASP.NET applications deployed in a farm of 4 Windows 2003 machines. Each application uses a separate App Pool and Virtual Directory in IIS. They rely heavily on sessions which are persisted out of process on a single SQL Server 2000 (<sessionstate mode="sqlserver" ... />). Applications are compiled against .NET 3.0 but .NET 3.5 SP1 is installed on servers.

Enabling sticky sessions on a load balancer

Any advise on this one would be greatly appreciated, I’ve been researching all morning and I’m still scratching my head. I started at a new company a few weeks ago, where I’m the only .NET developer as the development was originally done by an outsourcing company and I’ve been asked to research.
My knowledge of the existing system is extremely limited but from what I can gather the situation is as follows.