One horizontal line across the screen

Check and replace damaged component/s at its horizontal scan output section circuit. Check the LOT (Line Output Transformer) too for damage. Replace the horizontal scan output transistor. Check the input voltage to LOT. If the voltage is absent check the feeder resistor; if any. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts.
http://electronicshelponline.blogspot.com/
Type in this key phrase " my service table today " in the search box at the top right of the display window of the home page, to get gathered some pages which has the details of practical experiences to the author of that site.

How do I adjust the brightness of the screen?

Press MODE on the calculator.
Select Full on the screen.
You should now have a full screen.

You could also reset the memory.

**THIS WILL DELETE EVERYTHING ON YOUR CALCULATOR**

Press 2nd + (+) which is MEM
Go to Reset which should be number 7
Select All RAM which should be number 1
Press Reset which should be number 2

this happand when you dont use the Calculator long time
try the 2nd and Arrow up make the screen dark for 15 to 30 min
keep puse any key until will pass the 30 min
if it will not help than it could be the screen or the connection on the mainboard

Try to reset everything to see if that helps. If it doesn't , you can try to upgrade your operating system on the calculator to see if that helps to make it go away.
If that doesn't help try this:
"Remove one of the AAA batteries. Press and hold the [CLEAR] key. While holding [CLEAR], reinsert the AAA battery and then turn the calculator on. The calculator should display the message "RAM Cleared". Release the [CLEAR] key and then press it one more time to remove the message."
Let me know how it goes.

Make the calculator perform a self test: Part of the test is the display of some line patterns. You will be able to see if something is wrong with the screen.

TO PERFORM A SELF TEST (No I am not shouting, but I cannot use Bold fonts nor underlined)

1. Turn calculator ON
2. Press and HOLD the ON key
3. Press the "E" key , the key with an E to its right
   
4. Release the ON key
5. Tests will be performed cyclically until you execute a SYSTEM HALT

TO PERFORM A SYSTEM HALT

1. Press and HOLD the ON key
2. Press the and release the "C" key key with a "C" to its right.
3. Release the ON key
4. You should see the empty stack.

If you need to repair it, google FixThatCalc.
Good luck.

REPLACE VERICAL OUTPUT IC ' LA7838

Yes, the back up battery must be replaced.

Yes, this sounds like you'll need to replace your back-up batteries. That will probably resolve the problem.

I had the same prob with vertical lines on the screen, and getting messed up when there was lots of numbers on the screen.

Solution: Change your batteries. Put some freshies in then adjust your contrast until you see the little black box. If you still have a problem with the lines, darken the screen until it's black (2nd up repeatedly) and let it sit for a couple minutes. Lighten your screen back to normal (2nd down) and turn off then turn her back on.