I've been running around for 153 hours, when will I get to wear the Power Armor? Which quest will I need to finish??

Find the BoS and do there mission line with out getting a new elder, or get to the point were in the quest line, The House always wins. Mr. House will tell you the location of the BoS, but you will have to destroy them, so it is best to finish their quest line, by destroy i mean there is a terminal (Very Hard) that you unlock, once unlocked you will be able to nuke the BoS bunker, thought you will have a [censored] hard time getting otu due to 20 palidins P0WNING you, so dont do the The House Always Wins Quest Line. if you wont to live!

Get the companion Veronica head to 3 places like Repconn test site ( with the ghouls ), Silver rush weapons merchants in freeside.
Any other place of civilisation like inside McCarran, The old Mormon fort.. etc, she will have a little bit of new dialogue so talk to her at each place.
This will after three kick start her personnal quest to head to Hidden Vally, where you can perform multipule quests for the Brotherhood of steel.
After the last one when the lock down is lifted wait a few days then they'll offer you another to install something on blackmountain after this you get the offer of joining the Brotherhood and power armour training.
This is the easiest way, also just heading to Hidden valley by yourself may work as well, but require a test.

The other way is if you destroy the BoS at hidden vally without performing quests, is to get Arcade Gammon at the Old Mormon fort to join your party.
Visit everal places in the Mojave world map to do with tech or Enclave, then after a bit his personnal quest kicks off giving you a chance to enlist the Enclave remnants and recieve power armour training from them.

Thanks. I didn't know there's a Black Mountain quest after finishing the tests of the BOS. I went to Black Mountain and aimlessly flicked some switches related to radio broadcast but results in nothing. Now I know. I'm so lost, can't seem to jumpstart any NPC quests. All the conversation lines lead to dead end. @.@

It's quite confusing at first;
I rarely wear PA, so the first game I could not be bothered to look any deeper.

Just wait a week or so after getting the lockdown lifted by getting the items from the three vaults, then talk to the elder again and he should offer you tha black mountain task.