Thanks! Here is what I did based on what you said.
TL;DR
Pry the grey plastic end caps off the battery housing on both the port end and non-port end. Pry only the grey, not the black. Remove two screws from non-port end. Pry on the black plastic on the port end until the tray starts to slide out. Finish pulling it out by hand.
Mine looks good inside. It blinks when I used it to charge my phone, not when I recharge the battery. I'll see what I can find out, now that I got it open.
AL;WTD (Absurdly long; way too detailed):
At the ends of the battery, there are light grey plastic cap pieces. I used a very sharp knife and slipped it between the aluminum case and the edge of the cap. There is not much space, so the knife has to be pretty sharp. I used a multi-tool blade. An exacto-knife might work, but the blade should be pretty stiff since the caps are well glued. The caps a glued to a black plastic surface . It is possible to get under the black surface to pry. Do not do this! You want to separate cap from the black surface. Remove the caps from both ends. The end with the ports is easier because you a slip the blade through the opening of a port. It is glued down tightly, so when you start prying, the cap will flex a lot before separating. Put a bit of pressure on it and hold. The cap will gradually separate. I was afraid to press to much for fear of breaking something.
Once the caps are removed, you will see two small screws on the non-port end. Remove them. Pushing on either end did nothing. I had to start gently prying the black plastic surface on the port end, just like removing the grey cap. Pry and hold and the glue/tape will start releasing. The battery and electronics are in a tray that will start to slide out. Once I got it out a little, I finished pulling it out with my hands. After removing it, I notice that the black surface on the non-port end it still in place. The screws go through that, and into the end of the tray. Prying before removing the screws will lead to disaster.
You may scratch the plastic and aluminum in this process. Samsung probably has some specialized tools to open it cleanly. I got mine open with just a bit of acceptable scratching. A heat pad to soften the glue might make it easier.
So thanks for that info. It was VERY helpful. Once I got it opened, I saw the the battery leads were well soldered in place. I did not find any other obvious fault. I realized my problem is different to the OP's. My LEDs blink when I try to charge my phone with the battery, not when recharging the battery. It started happening sometimes with only one of the ports. It became more and more frequent, then started happening on the other port. Now that I got it opened, I'll see if I can figure out what is wrong with it.
