Try jump starting it off another vehicle, through the jump studs. Make sure the other vehicle is running with 2500 - 3000 rpm when you try and start yours. (Don't go for a 'weedy' car to jump start off either!) Use good quality, short thick jump leads, and give a twist as you clamp onto the terminals to ensure good contact. Connect up leads with engines off, then fire-up jump car and run for a few minutes before attempting to start yours. If it turns yours over but doesn't fire straight away, wait a few minutes before trying again, don't keep cranking! I was surprised at how small the lead is that earths the starter, I would imagine it could easily be overloaded. If car starts or cranks over jumping it, then you will know its your battery. If it still just "clicks" then my guess is starter at fault, or bad connection on to it. There are two big main positive wires onto it 1) direct from battery 2) ignition activated, they connect onto the same terminal. To check this terminal is tight, you can grab it with your hand, and see if it will wiggle...it should be solid! Reach down past the rear of the drivers side header, passing your arm just in front of the clutch master cylinder to get at it. You can see the starter by peering down with a torch if day light not good! Earth lead must be good also.
If your battery is completely flat it may have trouble running due to not being able to power the electric fuel pump, among other 'organs'. If battery has become flat for a while, or cold has got to it when flat, it probably won't be able to hold its charge, despite charging it, you'll need a new one. Also, flat battery = battery disconnect, and so engine will run / idle 'rough' for a short while until PCM re-learns it values.
Best V10 wishes.
(Don't be tempted to bump start, it will wreck your cats!)