Henley wrote:

Recently my kitchen sink started backing up into an old pipe. It was cut
and sealed outside at the main drainage pipe. Now the next joint up is
leaking. Do I need to replace the whole pipe or seal it? Could a blockage
in the drainage line be causing it to back up? I am worried because this
pipe is located against the wall of my house and runs thru my utility room
with the hot water heater and circuit breakers.

A blockage could well be causing it to back up and leak there.
Caulk it, maybe, as a temp measure.
Jim