That antenna is actually the service antenna but for these purposes it matters not. The broken antenna is not the cause of your no charge condition. I would suggest disconnecting and reseating the charge port connector to the motherboard. If that doesn't work, remove the vibrate motor and speaker from on top of the charge port flex cable and examine the flex cable for tears. I suspect the port is just not properly connected to the board. Unfortunately, that's not your big problem. Your real issue is that the tape you applied to the touch ICs is not going to fix that issue for long. I'm honestly shocked it worked at all but I can gaurantee your touch function's days are numbered. Think weeks not months. My advice is send it up to iPad rehab in New York. You can google them. Don't trust this repair to the guy down the street who spends his whole day replacing screens. You'll end up with a paperweight for an iPhone.
Have you tried disconnecting the battery and then holding down the power button for 10 seconds and then reseating the battery? You have to pry the motherboard up a little bit in the air to in order to disconnect the battery but it's no big. Also, have you tested with a different LCD?
Your MBP should be able to accept two 8gb sticks of ram but it sounds like either one or both of your new sticks is bad or, more likely, that the ram you purchased is not compatible with your laptop's motherboard. Just because it's the correct version of DDR does not automatically mean it will work in your computer. There are other factors like speed and latency, buffered vs nonbuffered, etc. My advice is to order your ram directly from the manufacturer and have them confirm beforehand that it's the right spec for your computer. In the meantime, just to be sure that the new ram is the problem, swap the original ram back in and see if the computer boots
Do this: 1) Unplug the computer and remove the battery (if it is removable) 2) Hold the power button down for 45 seconds 3) Without putting the battery back in, plug in the computer and press the power button. If it powers back up, insert the battery. 4) check back and tell me if it worked