If the backlight doesn’t work, try shutting the watch down (Settings-System-Shut Down) and restarting. In my experience the backlight doesn’t work about half the time immediately after the watch has been disassembled and reassembled, but power cycling almost always fixes the problem.
After reassembly, the watch will sometimes need a little attention before the display works again. You may need to either press buttons or attach the charger to jump-start the watch. Also, even if the display fully works, the backlight may not function immediately after reassembly. This is almost always fixed by shutting down and restarting the watch. You will almost never need to disassemble the watch again to get the display working, unless you forgot to reinsert the zebra strip or reconnect the ribbon cable connector.
There’s no need to desolder the battery. Use wirecutters to clip the ribbon cable as close as possible to the motherboard, then use the old solder beads to attach the wires of the new battery. Cutting out the old battery reduces the amount of heat the motherboard is exposed to. Also, the polarity of the battery is indicated by two tiny symbols next to the solder pads. In case you can’t read them, the positive wire is soldered to the terminal closer to the center of the motherboard. Finally, be aware that leaving too high a bead of solder above the motherboard will cause pressure and bright dots on the backlight when the watch is reassembled. Check your solder before reassembly and either melt down, cut or file off the excess solder to save yourself a second teardown.
These batteries are easy to find on eBay. Search for 402020. They are slightly smaller capacity than the originals, 120mAh instead of 130. Battery life is a little shorter than the original. I’ve seen people do all kinds of alterations to fit bigger batteries, like cutting the plastic frame or removing the safety circuit from the battery, but IMO it’s better to live with slightly more frequent charging than to risk a lithium fire from an overcharged battery. I don’t wait for the low battery warning on mine and still get a comfortable 2-3 days from a charge on my OG Steels.
Instead of desoldering the old battery, I clip the ribbon cable that connects the battery to the motherboard. Trim the ribbon cable as short as possible to the motherboard. The replacement batteries I’ve found have braided wire instead of a ribbon cable, so they can be resoldered to the pads that the remnant of the ribbon cable is attached to. Pebble used enough solder that I’ve never had to add any - just melt the solder that’s already there and drop in the new wires. You can tin the wire ends before attaching them to make a better connection, but you get a good solder connection even with the bare wires. Make sure you get the polarity right - the positive (red) battery wire attaches to the pad closer to the center of the motherboard. If you look carefully there are tiny + and - symbols silkscreened into the motherboard just outboard of the pads.
I did the same - broke off the charge connector. The trick is to remove the plastic frame by pivoting out the 3-button side first, and put it back in by putting the one-button side with the charge connectors first. That way you’re not forcing those thin metal contacts past the frame. They don’t often break, but they did for me one time, and the watch will not charge after that.