Something ain't right here, diagram shows the red belongs on a start capacitor but your compressor looks like it has been replaced at some point, and a non-capacitor compressor was used. The upside down configuration is ok as long as the pins measure out ok, you need to measure continuity between the 3 pins and to ground to rule out an electrically failed compressor.
Gravel bases have not been used for a number of years. If your resin is not caked, you are likely wasting your hundred bucks. If you do, make sure you don't fill the resin tank completely - the 13 inches of freeboard is required.
When you receive your lower distributor, check the length against the old one as the replacements are all one length and may need to be cut to the proper length. I always seal the bottom area where the foot valve connects to the tube with silicone (and allow to cure) this will prevent it from twisting and opening up to allow beads to enter.
To push the valve down into ghe resin, connect a bose to a faucet and run the water into the middle of the tube as you push it down - that will alow the valve to push through the resin without damage.
The nozzle venturi assembly should be replaced as the washers inside compress and reduce suction during brine draw.
You need to have your tank to atmospheric pressure (14.7 psi) - drain the tank completey, then depress valve for a minute, the static pressure in the room will fill the area between the bladder and tank, then when the tank (bladder) is full - the atmospheric pressure will act as a cushion to dispense water. The unit will take up to 24 hours to fill the tank, so a gallon or so will be available. If you require more than this, fill a container and refrigerate and repeat process. while the unit is processing, you will hear a slow dribble of water down the drain
You could try swapping the rotor with the lower drawer to test, often the upper drawer gets used much more than lower and thus greater wear. Also check the Y connector that gangs the 2 drain hoses into house drain, could be sagging and partially blocked if not secured well.
On your storage tank ther is a schraeder valve, this is to allow air pressure between the wall of the tank and the bladder so that it will build pressure to dispense - open the produ t water valve and allow it to fully drain the tank, then depress the schraeder valve so the tank fills to atmospheric pressure. Allow approx 24 hrs for the unit to process a full storage tank then you should be OK
Did you replace the membrane at the same time ? It is important that you install that in the right direction.
At one time, softener parts were available through RepairClinic, but the numbers do not work for me right now - the part numbers you will require are as follows: Lower Distributor 7105047; Seal Kit 7129716; Nozzle/Venturi ass'y 7187065.
Generally speaking, resin does not "wear out" as it is used for ion exchange - unless you have some nast iron etc in your water. When that is the case, the resin bed becomes caked and hardens into a mass and does not flow freely. The high efficient resin refers to the fine screened resin, it is the surface area of the resin beads that determines the efficiency - regular resin will do the same job as high efficient, you just need more of it since the normal bead size is larger than the finer beads. The resin in your unit is cation resin. If the lower distributor became plugged, then the small beads have gotten through the screen of the distributor, and it should be replaced. Do hou havd at least 12 lineal feet of plumbing between softener and hot water tank ? If not - hot water can leach into it and disfigure plastic parts in the softener.
I believe your unit is a 1994 model, and if it has never been serviced, the valve is due to be re- sealed, the simplest way to replace resin is to change out the resin tank (approx $400) and should not really be considered as a whole new softener is likely in the same price range. The tank is not supposed to be full to the top with resin beads as it requires this "freeboard" area to properly flush all of the beads during regeneration.
Easy way to test if pump will alternate to upper arm - after it has filled and is washing stop it by clicking the door open and quickly close it again (not a long pause a few seconds) - the swishing sound of the water will audibly change if the upper arm is indeed activated. The timer itself does this, but only ever 5 min or so, may need to sit down and read a book and listen while it runs - it is not unusual to see these timers fail to where they no longer pause, or pause too long.