macbook shuts down immediately after startup
To verify your problem I need you to post the Battery status in detail.

Click About this Mack (top left) > Syst report > Power 

then copy the battery information in your original post.

To preserve some power consumption, open syst pref > Energy and disable the Power nap in Battery mode.

To verify is some process is keeping your Mac awake (dark mode) and consuming power open Terminal and paste following 

pmset g  and post the info here

also run pmset -g assertions and post it here

Under normal (perfect) condition the battery should last 1,000 cycles, but that is not always the case, so your are getting close with your 700 cycles