The max ram on a M960 / M970 / M961 MB 224X motherboard is 16 gb ddr3. That is the series most common with the vpc series.
Either find the spec list of your model or disassemble everything and read it on the body of the parts - as in what they support. Don't do it if its under warranty though. Talk to the service center guys.
As for as only 1 ram port working, are you sure its the port and not the ram itself? Because if it's the port, which is hard welded to the board then you have to replace the entire board.
Also make sure you are running a 64 bit windows because 32 bits don't support more than 4gb.
Do let me know if your Laptop has been ever upgraded before, I have something to troubleshoot and I could use your help; since you and I have the same series' laptop.