Can anyone explain to me how the P/E ratio is a meaningful metric for a company's stock price and what it "should be" at when that company does not distribute earnings to the shareholders?There are two ways to gauge the value of a company. One way (the way to which you allude) is to buy it and hope that in the future, someone thinks it's worth more than what you paid for it. Some people call this the Greater Fool theory.
The other way is to treat owning shares like owning part of a business. (You might hear about this as the Graham-Dodd or Graham-Dodd-Buffett model.) In this case you consider the value of the company as the current liquidation value of the company's assets plus the total amount of free cash the business can produce over its useful lifespan.
The math of that valuation gets a little bit interesting, because if you project the free cash growth into the future ten or twenty years, you can use a present value calculation to get a fair price for the company right now. Divide that by the number of outstanding shares and you get a target price per share.
One of the flaws of this method is that you need to have a sane sense of the growth rate of free cash, so you'd better base that on a stable and measurable history, and you have to verify that against sanity and the company's published plans.
Graham's real insight was saying "If you do all that work, also add a significant margin of safety to account for any flaws in your calculations."
Of course you shouldn't use reported earnings for these calculations; they're far too easy to manipulate under GAAP and accrual accounting. Even so, finding realistic numbers and ruling out most stocks as overvalued is relatively easy.
(I'm working on a financial analysis site right now.)