Sounds like something went wrong during the update, leaving you with messed-up software. The black screen/red triangle is recovery mode.
Just in case, try forcing a shutdown by pressing and holding the power button until the home/back buttons start to flash and then the phone reboots. If you are really lucky that might clear something, though I doubt it.
I also doubt that there is anything much you can do using recovery, but when you have that screen up try pressing power and (I think) volume up together (otherwise try power+volume down). That should give you a menu of options. There will be an option to apply an update, which you could try in case it can still find the update file (try charging the phone incidentally). If it can't then erasing the cache is harmless, but probably won't fix it. A factory reset will erase your data, but if the system software itself is corrupted that still won't help.
Most likely you'll need to reflash the phone. This is done using something called a ROM Upgrade Utility (RUU), but since those things only work if the software version and "customer id" (i.e. region and branding) are right we'll need to know which country you are in and which network (if any) you bought the phone from. Then we can see whether we can find something suitable.
Of course if it's still under warranty (which it should be in the EU, as that's 2 years) you could get HTC to fix it. If we can't find anything else you can try that anyway - after all, if it was an official update which did this there's a good case that they should fix it too!
I'm assuming in all this that the phone software was not modified (i.e. you've not rooted the phone before taking the update).
