There is no queue.  MSDE has a queue when more than 5 users are connected, it slows down on purpose.  SQL Server Express no longer has that constraint.

2GB of RAM is the OS limitation (Server 2003 Standard??), otherwise you can configure the RAM usage in SQL Server Enterprise Manager to use more.

1000 simultaneous connections is too much one CPU, you need to figure out a load balancing scheme or get a multi-core machine.  100 is the recommended limit on a single CPU, (1GHz). 

Check your CPU perfomance and see if requests are being queued there.

You should also run the sp_updatestats 'resample' stored proc., if performance has been decreasing over time, and see if that helps, because the stored procs use the statistics as part of the creation of the execution plans.  But the problem sounds like you have too many users and not enough horsepower.