Line across top of screen

Normally horizontal line [a thin vertical line across the center of the screen] fault with CRT based TVs is the fault with its vertical scan output section circuit. 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. 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.

If you wish to get some details; check the site linked here. Pull up older posts. Surf the site with patience. http://electronicshelponline.blogspot.com/
Line, faults & possible causes to LCD & Plasma screen are given with illustrations. You can get an idea about the fault to an extent.
Type in the brand name to your device, in the search box [at the top right] of the display window and the Search will start at once as you type in, and will show you all the related posts. It will make surf easy.

When hooking a super Nintendo or an NES system or a sega genesis system to a digital tv you need av cables for it to work then instead of using an rf switch

Did you say HDMI? I don't think there are HDMI plugs for Sega Genesis. You can plug in your Sega via composite video through RCA cables (yellow, red white) or via RF signal through coaxial cable. Check your TV's specs to make sure it can display standard definition content via composite or via RF.

You can double check to make sure your Sega Genesis is working properly by plugging it into an old-fashioned CRT (fat tube) television set.

Well mabe its broken buy now so you could buy a new one then.

This is pretty common. The games just need a good Q-Tip cleaning, and then the weird clean pencil-eraser rubbing.
Get out a Q-Tip, and rub it inside the game, on the copper part (The part you stick down into the system.). Keep doing this with new Q-Tips if the old ones get soiled with black stuff. After the new Q-Tip comes out white, it should work.
Sometimes, that isn't enough. Use some Windex or any other rubbing alcohol, dip it onto a Q-Tip, and rub it onto the copper part. Then, use a dry Q-Tip to dry it off, and let it sit out of it's case and out of the system for about 20 minutes so that the alcohol dries.
If that doesn't work, use a pencil with a clean pink eraser at the tip. Rub it inside the game, and use a Q-Tip to get all of the eraser shavings out. This breaks the electro-static cling/friction made when the game is being read by the system.
And if none of that works, go on Amazon or Ebay or to the store Slackers and get new video and AC wires for the Genesis. Sometimes that's all it needs!
I really hope this helps!

picture tube needs to be replaced

The line is actually part of an unseen border.

intermintence in vertical IC deflection its a job for experienced tech need to look for that circuit and do fine job resolding that IC

yes unfortunately i think its been dropped by the sounds of things,and yes it can be repaired,you can purchase a screen off ebay thier not that expensive,if you know anybody thats electricly minded if so let me know and i'll send you the webpage that shows you how to do it step by step.dont send it away to be mended what ever you do because it'll cost more to repair than its worth.