My iPhone 4 is dead. I charged it for an hour then tried the power reset but no joy.

I will assume that your iPhone 4 is not in warranty, otherwise you'd already be at the Apple Store, right? I will also assume that you aren't interested in paying the $79 battery service or the $199 iPhone 4 Out of Warranty swap price for a device that is worth less than $100 (US prices)

So then let's troubleshoot.
When was the last time that it was working well?

An iPhone 4 is pretty old, and if it has been dormant for some time, then it is possible for the battery to lose charge below the level at which it is able to charge. The battery has a teeny little logic board buried in the wrapper of the battery that dictates the charging process. If there is really zero energy, the battery does not have enough juice to be able to tell itself to charge when the charger is connected.

If the phone has relatively recently been working well, then start troubleshooting at the charge port. Is your charge port clean? Try cleaning it with 99% alcohol and a q tip. If that doesn't solve, then you need more information---there are really handy inexpensive little usb ammeters that you can plug into a charger and then the device and it will tell you exactly how much, if any, charging current the device is pulling. An iPhone 4 with normal charging system should pull about 1amp. If yours is pulling 1amp and still not showing a display, try connecting to iTunes to see if your device is recognized. If it is, then you need to troubleshoot a display issue, not a charging issue.

If yours pulls closer to 0 amp, then you need to open your phone and troubleshoot the battery and dock connector. Lots of DIY resources out there to help you with this, just a google search away.

A quick trip to an independent repair shop will also help you drill down on the problem. Pick one that stands by their work with great review, great warranty and someone who is willing to look at this iPhone 4 with a no fix = no fee policy.