I have a 586E case forklift that is stuck in forward gear and when in neutral still goes forward and when put in reverse locks up. This machine has been is storage for about 3 years.
My first thought was, IF the transmission was okay when the machine went into storage, you may to remove and clean the transmission control valve. It's not too complicated to remove it, just take care when disassembling it that all the little springs and spools don't get lost.
If that doesn't correct your problem, the forward clutch pack may have welded together.
That means a removal of the shuttle and a rebuild.