Yeah true about that. Despite that, L had the full force and power of the whole Japanese police to begin with
No, Light had 5 people from Japanese task force and neither of them were anywhere near the level L, Light, Near or Mello. They were just simple detectives. Hell, if it wasn't for his dumb luck, Light would have lost to Naomi Misora (Raye Penber's fiancee).
and his only task just to find kira[light yagami] a dorky teenager [at that time] using a notebook he accidentally discovered.
You're saying it like it was as easy as pissing on your finger. Light wasn't just some "dorky teenegar", he was easily one of the smartest humans in the world. A natural genius. L started from NOTHING and had to work against supernatural powers that he knew nothing about. Despite all that, he still cornered Kira and would have captured him if only he had more time. In fact, he knew Light was Kira from the very beginning, he just didn't have definite proof. At one point he obtained it, but then Light pulled that amnesia and "victim of the Kira" crap. That was a small setback and in the end L still found a way to prove that Light is Kira, but he ran out of time. You can't really say Light won, when the guy had two friggin gods of death on his side, whom he forced to lie and even falsify the rules in the book.
light won against the so called "best detective in the world" with his powers of deceptions and mind games.
L didn't lose to Light, he lost to magic. Plain and simple. He knew Light was Kira and he knew Light would kill him. There was just nothing he could do against magic. He already prolonged his death as long as possible by outsmarting Light from the very beginning. L was on the offensive, Light was on the defensive. He only won due to the fact that he had a major head start over L.