Why is my keyboard only partially working?

My 13" MacBook Pro Retina (Early 2015) stopped responding for a second time, and I am looking for advice on what to do next to get it working again.

The first time it stopped responding, the battery had been bad for a long time, but the machine kept working while plugged in. Apple support refused to change the battery due to units age. So, I decided to try and replace the battery with an iFixit battery replacement. This brought my system back to life!

As soon as the install was completed the MagSafe connector was plugged in, the unit and the login screen appeared. I did not try to login, given that the instructions encouraged charging to full and then for two hours more. The light on the MagSafe connector turned from orange to green and stood for two hours.

Screen was now dark again and would not respond. I unplugged the MagSafe and swore loudly at the universe. I have since reattached the MagSafe adapter and discovered that each time the MagSafe adapter is attached the screen lights up.

However, I cannot login as the keyboard is only partially working. As I cannot see the characters, I cannot say whether the correct characters are appearing when the key is pressed. I have been able to establish the following typing in the pw entry box on the login screen. These keys appear to be functioning properly: a,s,d,f,g,h,j,k,l,q,w,e,r,t,y,u,i,o,',space, delete, left and right arrow keys. These keys work, but double characters appear when key is pressed: z,x,c,v,b,n,m,,.,1,2,3,4,5,6,7,8,9,tab,Fn These keys appear to be not working: Power Button, 0, shift keys, caps lock, return,-,=,;

I'm saying shift keys do not work because login has a capital letter and when typed, it is not succeeding. I'm thinking that this keyboard issue could have been the problem the first time I could not get the system started as well, but I'm not sure.