How can I check Google Page Rank of all pages of a website without installing any tool on my machine?
I honestly wouldn't bother doing it all. The publicly available toolbar PageRank is only one of 200+ factors Google uses and it doesn't necessarily reflect where your page will appear on the search results pages. It's not updated very frequently either (every few months), while the actual search results are updated daily. At best, it's a not very useful barometer of how Google views your site.
Beyond just basic SEO best practices, you're far better off focusing on improving your website's usability, content, and actual conversions once people get to it than by wasting time checking PageRank constantly. It's important to remember the purpose of your website's existence. If it's to make you money, focus on improving that, not on improving PageRank. PageRank doesn't directly make you money. If you're concerned about getting more traffic, use social media or advertising. PageRank doesn't directly bring you more traffic.
At the end of the day, PageRank probably can be improved and manipulated, but if that's your primary focus, what is the point? Your only reward for hours or days of work is a bigger green bar.
Focus on what matters, PageRank will take care of itself.
All that said, this might be what you're looking for if you want to waste your time.
Edit in response to DisgruntledGoat's comment:
Agreed. The publicly available PageRank isn't the same as the internal ranking. I'm not sure why Google even keeps it available. The internal PageRank is what actually ranks the pages, but the only way to check that is to see where your site is on the actual search results page. Checking the results themselves every once in a while isn't completely useless, but it fluctuates from day to day or even hour to hour, so you can easily drive yourself crazy doing that too frequently.
In my opinion, it's far more useful, time-efficient, and cost-effective to focus on on-site SEO, marketing, advertising. After all that, however, if your page doesn't get your visitors to do what you want them to do, what the page was designed for, all the other effort was time and money wasted.
In regards to is pr still a important i think that although it may not be as important as part of the ranking algorithm i think that as a webmaster its still a really good starting point when looking at a pages authoirity as some of the signals that will give a page good PR will also be the same signals that search engines are still looking for.