Toyota Hydro Assist Weird Problem.

[Piros 1]

My thoughts, is it possible to flip the cylinder and reverse your hoses so the cylinder is working in reverse order of its present position? If so and you have the same issue turning left then it is obviously in the assist cylinder but if you still have issues when turning right it is to do with your steering geometry or your gear box.
If your pump were bad I would think it would have the same issues turning left or right.
My thinking it is in your cylinder and you will need to pull it down and see if it has a bent rod or an internal issue.

 

[OnlyOneDR]

The pressure to work the ram is directed from the valve in the steering box. I am going to assume you tapped your own box. It is possible when you tapped it that a loose piece of trash got in the line/fitting at the steering box that is blocking fluid flow? When you unhooked everything and worked it manually that one time maybe the trash dislodged and floated around that side of the box until it stuck in the fitting again? Your issue sounds like something is blocking the hydraulics from pushing on the ram, not that the ram itself is locked up. To bind up entirely would require the hydraulics essentially fight from both sides. If you have a spare steering box you could also try swapping that.