Laptop doesn't start if charger is not plugged in

Solution 1:

I got an old Lenovo z50-70. It was mostly used with a charger as previous owner says

If a battery is left at 100% on a charger, it will eventually die. It is doubtful the owner would have known about Battery Threshold charging, indeed the old machine may not even support that.

So at this point, based on your own description, the battery is dead and needs to be replaced. If the battery were good, it would charge, you would know that and it would start on the battery, but it does not.

So until you can purchase a new battery, you will continue to need to leave it plugged in.