あげく => to end up; in the end; finally; after all ~ N2
てあげてくれ => to do for; to do a favor N3
Coercion
たあげく => After A, B was the final/end result N2
Reason, Result, Response
...てあげてください => to do for; to do a favor N4
Benefit
げ => Looks A N2
Adjectival, Descriptions
あげる => ...Up (Upwards) N4
Direction
あげくのはてに (は) => finally; in the end; on top of all that N2
Result
おかげだ => thanks to... N3
Cause, reason
上げる => to finish doing ~ N3
させてあげる => (Allow) N4
Allow
げ => looks like; seems like; appears to ~ N2
にあげます => give, take N5
Give it away