32-bit Enterprise SQL 2005 on 64 bit Windows 2008 Server Standard. Memory configuration
The server has 64GB RAM installed, however in taskmgr there are only 32GB available. I believe this is a Standard Windows Server limitation, just want to confirm.


You are correct max memory limitation for Windows Server 2008 Standard is 32 GB. This is mentioned in Memory Limits of Windows Server Machines.


  On other side, we have checked the SQL Server memory counters on perfmon, and the value we get for target and total memory is about 3.500.000,


When 32 bit SQL Server is installed on 64 bit machine it is called WOW System. For this the Virtual Address Space limit is 4GB. And in normal and default configuration SQL Server cannot see/utilize more memory than the VAS limit so you are seeing 3.5 GB in Perfmon counters.


  The service account is Local System, but I cant see the "Using locked pages for buffer pool" in the SQL Server logs


Since you are on 32 bit system you should not look for this message instead look for "Address Windowing Extensions is enabled", if you see this then it is enabled. If you have 64 bit system then the message "Using Locked pages for buffer pool" makes sense. Actually this is how AWE works in 32 and 64 bit respectively.


  As this is 64 bit OS, no need to enable AWE.


No, this is true for 64 bit SQL Server not if you have 32 bit SQL Server.

Now for SQL Server to see more memory, you have to enabled AWE so that SQL Server data and index pages can see more memory than 4 GB. Since your windows can see more than 4 GB( In your case 32 GB) AWE would help SQl Server data and index pages accessing larger part of memory. Please note I mentioned data and index pages, apart from this no other memory consumer can see those extra memory. 

PS: At the time of writing the answer most of the blogs.msdn links are not opening as they are being migrated to new platform, I will add the links in answer as soon as they start working so that you have some reference to read