Take out the battery and examine it. Next to the 3 contact points, there should be a small square sticker.
If that's white, you may be in luck. Note the word "may", as there is another sticker hidden inside the phone itself.
However if it's pink/red, the phone has got water damage indeed. In that case, your warranty will be void.
I'm pretty certain that'll be your case, as you mention having water inside the rear cover.
In the past, HTC would have replaced the motherboard at your expense, but nowadays a new unbranded Desire is actually cheaper than the price of that repair.
So don't even bother sending it in. Just get another one. I'm not kidding, it IS cheaper than getting this one fixed. HTC doesn't even repair Desires anymore when there are signs of water damage. (and here
's proof of that, as it has already happened here)
I'm sorry I don't have better news or some secret trick to get it working again.
For the record, I'm not a HTC employee, so I gain nothing by telling you to buy another phone.