mobiusstriptech

No it won't work without the capacitor.

I agree with the previous comments. Clip down the legs as close as you can. Either you had leakage or you managed to burn a number of areas. C85 looks like one leg is not attached and like the pads are gone. C48 looks like there is some kind of damage, like burns, to a number of traces under the legs. C44 and C45 look like there is lots of damage on the pads and surrounding area. When dealing with potentially leaking electrolytic capacitors, you should always give the board a really good wash with the strongest IPA you can get. At least 91%, but higher is even better. The dielectric is incredibly corrosive and it won't take long to eat through parts of your board. The other part is that some of this honestly looks like burns. What type of iron/tip were you using?

Yeah it's hard to tell with the picture quality. How did you clean the board when it was recapped and did you clean the entire board or just the area around the pads?

Sounds like a sync issue. What output are you using? Caps aren't common on Sega consoles, but I have seen them go bad before. Honestly I have seen issues like this from dirty cart slots as well.

I have seen that circuit cause issues before on some 2600's. That is a pretty common circuit that will generally work, but it's not technically correct. Usually what happens is the output is not properly attentuated and the tv you are hooking into is sensitive to the signals being off. In those cases, the console might work on some tv's and not others or display in the wrong colors.

Swapping the screen to another of the original screens can be tough if you don't have the correct tools. Usually when I have seen issues like that in the past it has been an issue with the driver or from left over cap residue that damaged other components. If you are dead set on using that system and don't mind losing the portability, you could consolize it was a GameGear TV mod. However if your issue is more than just the LCD driver, then you might still have an issue. Do you have any pictures of your recapped board?