Fast ranking website in google question

Hi, I have a question regarding Page rank and google. I recently bought a domain targeting low keyword competition niche. I have done on and off-page SEO in addition to getting backlinks, but it STILL isn't doing well on the google ranking. Is this because the domain is fairly NEW? Does it take time for your website to increase Page Rank, regardless of all the SEO you do?

I want to buy another domain to target another niche, but should I try and find an expired High PR blog, buy it and then use my new domain?. Will this help my website to move up google's page rankings faster?

Sorry for the newbie question, I'm still trying to wrap my head around how PR and domains work.

Google does PR in periods so it updates them all at a single time - you might have gone up but you wont see it until they update it all.

Yeah buying high PR old domains is good but you want to make sure they PR hasn't been faked first as this is something that can sometimes happen. Also make sure the domain hasn't been de-indexed or received penalties before..