I have this same problem.
The screen would go on and off depending on how it was tilted until it eventually just stop displaying anything but white. Now and then I get a few green lines though depending on the game.
However, ultimately I lost interest and just stoped playing it cep't for GBA games now and then.
The cable always seemed so hard to find.
However.
deal Extreme has one for mega cheap and supposedly in stock now too. (man I wish they would organize their crap a little more, I had to dig for it, dunno if it was there before or not, but it is now :3)
http://www.dealextreme.com/details.dx/sku.15855
I have yet to buy one just yet.
I need a better touch screen too though.
So I just end up putting it off.
Maybe after I get me an EZFlash V or something.
Anyway
Go buy one of those and repair that sucker up.
Just remember not to try testing the screens while its open and accidetly flip the battery the wrong way. Ya I did that >.>. Fixed it though but it was indeed bad. (I was hoping I could bend the cable about to see if I could get it working in a taped down position)
Oh and a new screen wont fix your problem. You need a cable.
If the cable doesn't help then go for a screen as its the only other possibility.
I'd also suggest getting two just in case since its on the cheap and rather rare.
Good luck and all that.