Ok so you didn't call 2 Men and a Truck? They specialize in this.
Seriously, do you own the plot? And make sure rent is paid up on it. This could be why the unpack is greyed out - if you don't own the plot.
Place the crate in the plot on the ground - that should make make the "unpack" light up to use. That should deposit all the items from your crate into the plot storage, making them available for placement if desired.
Only one crate can be place on a plot