Pr update takes time for any new website. if google found your website interesting to give a pagerank then it will surely give it to you but for that you have to do continuous seo for your website.. link-building process gives a very nice effect for the google pagerank update.
Alexa ranking depend on your traffic amount and PR depend on the dofollow backlink So, basically they dont have any relationship, mean your alexa ranking will never affect you PR and vice versa
Is your website new? Donot create any relation of your website's alexa rank with page rank. Both are different. You can only increase the page rank of your website by quality content, internal link structure and backlinks from relevant websites.
There are so many methods to increase the Google PR - 1. Unique Content 2. Proper on page optimization 3. Quality back links :- Forum posting, directory submission, article submission, blog commenting, social bookmarking, theme based one way links. 4. User friendly Navigation
PageRank has nothing to do with your Alexa ranking. Your alexa ranking is a measure (and an inaccurate one at that) of the traffic your site receives. PageRank used to be a measure of authority and likeliness that a "random surfer" would come across your site, but now, despite the focus the IM community puts on it, it's really not that important. If you still want to get PR just build dofollow links from high PR pages. Blog commenting can be a good way to find pages with PR that you can get links from.
Either you have a ton of nofollow links, or toolbar PR has not updated yet. Check gain now. Last update was July 15 from memory.