Got everything plugged in, programmed the TV (an old Hitachi 27ax2b) just fine. But we were having problems with the cable company turning everything on, also had to do some moving. I unplugged the box, and when I plugged it back in, the remote would not do anything to the box, not even make the light for "remote" flash. I then made the mistake of using an old post to attempt a fix. Used the 980 and 981 to attempt a fix, and probably reset the whole remote.

The remote we have is Silver with a Red O.K. button and a Black on Demand button.

Any help would be much appreciated.

Also, the Box now shows the Power light on, and all we see is a black screen.

Use 982 to turn off cable setup code lock, and then assign 01982 to the Cable button.

No dice. Does a Dark Silver/Grey remote change your answer on the code? It doesn't work on the set-top or the tv. Oddly enough, it did work on an older "light" silver remote from another set.

All red button Comcast remotes have setup code 01982, and 01982 will control the RNG-110.    
Did you get 4 blinks when doing 982?  2 blinks when assigning 01982? Please try it again.

Your TV should respond to 10145, 11145, and 11960.  YOu do need to assign that to the TV mode.

All I get when assigning the 01982 is one dash. I DO get the 4 blinks with 982. I know this shouldn't REALLY make a difference, but it does say xfinity on the remote.

There's a couple of things to try to understnad the problem.

Use the 983 commnad to blink back the remote's signature. It should be 3039.
Then, let's check if you can assign any cable setup code.  Try 01376 to see if you get 2 blinks.  
Are you able to power your TV on and off?  That would show that you can get the remote to accept some setup code.

At some point it may be worthwhile to do a 981 reset again (should get 4 blinks), follow that with a 982 (this is a toggle setting-- the remote needs to be in the state where it has blinked 4 times and not 2 times), and then assign 01982 to the Cbl button.

If you still get a single flash, 

Check on the 3039, and the 01376. Nothing happened until I reprogram it with the appropriate code (10145 hitachi tv) Still no control on the Cable.

"reprogram it with the appropriate code(10145 hitachi TV)"??  The TV setup code shouldn't have been altered when trying to assign 01982. Let's make sure that we're on the same page:
1) Press Cable
2) Press Setup until 2 blinks 
3) Enter 01982
The remote should blink twice.

Then,
1) Press TV
2) Press Setup until 2 blinks
3) Enter 10145
The remote should blink twice.

Yes to both. TV control is a go. Cable control is a no go.