Culligan Medalist Plus won't REGEN

Recently moved to West Virginia. We have NEVER owned/operated a water softener system.
Our local CITY water is hard. The following was installed in the fall of 2013.

CONFIGURATION:
Part #01020370: Culligan Medallist Plus (Gen 2) water softener
Part #01016369: Resin Tank (Tank, FG, 10x40 ACME, 1"Man, 1.0CF)
Part #01018705: Brine Tank (16x40 Beige BTASY 474 Culligan)

SYMPTOM(s):

1. white film on various faucets, 'dusty' dishes after dishwasher is complete
2. hot water kettle has floating -and- sinking residue... EVEN when we use Brita and Pur filtered water.

DIAGNOSTICS:

1. brine tank has salt (no bridging) and wet/brine at the bottom.
2. AccuSoft valve control system
   1. Receives 24 VAC power from the wall-plug PwrSupply (actually 29.x VAC)
   2. Allows me to:
      1. Adjust settings
      2. Inspect Statistics
   3. but REFUSES to:
      1. drive a REGEN process (via a LONG press of the REG button)
      2. enter the DIAGNOSTICS menu ('+' at the BLANK screen)
         1. instead of 'home' I see an 'upside down telephone icon' above a BLINKING "REG", followed by a "u 00"

I never hear any 'mechanical movement attempts' or 'buzzing/humming' (of any kind).
I have tried the following:

• unplug the power cord, wait a few minutes and plug it back in (no joy).
• unplug power cord, unplug battery backup, wait 15 seconds, replug battery into control board, replug power cord (=> didn't change anything; even the statistics remained the same)

SETTINGS: tod (accurate) tor (2:00) REG (tcb 7) SLtP (7.0) Buu (10) Br (45) CAPG (250)
STATISTICS display: Flo (0.0) galr (0) 14day (0) day5 (181) totl (204)

The brine tank (shining a flashlight) seems to have about 27" of dark (resin?) beneath the 9" of (water at the top)... ignoring the rounded top of the tank (i..e. the 36" is floor-to-curve as the tank curves into a 'bottle')

Can anyone tell me:

1. What's most likely the 'root cause' of this errant behavior? (seems like it's gotta be the control board, but possibly a 'seized water valve'?)
2. Is there a 'previously used' (junk yard/salvage) market where I can purchase a previously working valve control board?
3. What ratio of dark/light should a flashlighted tank show with:
   1. brand new (or freshly re-bedded) tank
   2. "resin" is dead (in-effective, time-to-replace/re-bed tank?
4. Is it worth re-building a 10-year old Culligan? (I find it troubling that something with a 10-year warranty, dies at 10-years... ... but I didn't own it during that time, so cannot know how well it was taken care of... the Culligan guy said he had no record of any service calls to this home)

Thanks, in advance, for any knowledge/wisdom you may be able to impart on us.