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The first hour or so of charging a totally dead (as dead as you can get a lithium ion battery, which isn't actually totally dead) doesn't even give it enough charge to die when you try to turn the phone on. Leave the charger plugged in for 24 hours - without trying to turn the phone on - and see if it comes back.
To get the maximum life between battery changes, you charge the battery when t's at 40% to 60% discharged. To get maximum life between charges, you discharge the battery almost all the way - but that GREATLY shortens the life of the battery. If you've been doing it that way - discharging almost all the way before recharging - 2 years is a long time for the battery to keep running. You should get between 100 and (if you're very lucky) 250 charges that way. That's a year or less for most people. If you recharge at about 50%, you can get well over 1,000 charges. So you're probably due for a battery replacement.
It's a balancing act. Due to physics and chemistry, you can't get both long battery life and deep discharge from a lithium battery, but that's the highest density power source we have now, so it's what's used in phones. (A lead acid battery would be much better - but do you really want to carry a 10 pound battery around to power your phone? Even a gel cell lasts longer when deep discharged, but it's not that much lighter.)
We're going to have to wait for powdered silicon anodes before we see any major improvement in cellphone batteries (unless someone is working on something I haven't heard about yet), but that's years in the future.
(And it's one reason I won't buy a phone with a non-replaceable battery. I've spent years repairing phones, so I could replace the battery, but I'm getting too old, my hands aren't that steady and my eyes aren't that good, so it's a lot easier to just pop the old one out and push a new one in.)