Angel:
I'd rather have a working screen
....
That strip could be wired in so many different ways that you may never quite get it right.
I'm presuming you've got some experience in this sort of thing, but I'll lecture anyway
....
When you're lighting up an LED these days (especially with a blink), all kinds of goofy stuff can be used to do it. You can, for example, power the LED directly from a "main" feed (3VDC and up), and switch the ground by way of a "driver" IC or a couple components (one or two transistors). Or you can ground the LED and switch the voltage to it the same way.... Meantime, the "feed" from whatever's telling the driver components to light (or turn off) the LED can be of either polarity, and from about any source. The blink, for example, could be coming from a microprocessor (there's at least one) that's handling the timing of the blink, or the steady state, and hitting the driver just for the extra current.
Or there may be no driver at all - the processor could be capable of driving the LED by itself.
Or the steady state action could be one driver, and the blink coming from the processor, or vice versa, or....
(I'm just getting warmed up....
)
IMHO, it's still likely that a bit of crud or a solder ball is the real culprit, but finding it could be fun, and it's probably not worth the effort. If you have the itch to pop out that little board, look for semi-microscopic crud - green stuff, etc., an solder balls. Might get lucky....
Reminds me of a friend's kid, many years ago, who tossed his dad's Motorola HT (Ham Radio) into the toilet 'cause dad was yakking on it too much for the kid's choice. Once my buddy cleaned and dried it, it worked better....
Or the time my daughter jumped into a pool with a brand new phone in her pocket, 2 days before heading off to a couple weeks at a camp. I grabbed the phone, cleaned and dried it, to no avail, and ended up buying her another one (I was a very wealthy man until my wife found out about it
). The old one sat for three or four months, and I happened to notice it one afternoon. A partial re-assembly, just for the heck of it, gave me a working phone! The wife had been asking for a new one, so I put it back together and called the carrier to activate it for her. It's still working, although "retired" for quite a while. (I think it's Analog, so it's not going to do anything useful anymore, but that's another story.)
Good luck!