The thread title says "HTC Sync Manager", which is not the same as HTC Sync. For the Desire you probably want the older HTC Sync, which last time I looked you could still download from HTC, so you could give that a go instead if sync Manager is not working.
Secondly, the phone does have usb debugging. Maybe you've not turned it on, but it's there. Look for developer options, if I recall right.
But if all you want are pictures and contacts, well pictures should be on sd, so you can just copy those over usb with the device in disk drive mode or else using a card reader.
As for contacts, if they are synced with Google you just resync to the new phone. Otherwise, just go into the contacts app and save export them. That saves them as a .vcf file which you can copy to the new phone and import. No need to worry about sync software, and then finding sync software for the new phone.
BTW if the new phone is a HTC, they now come with some data transfer tools which can be used to copy stuff straight from the old phone via WiFi.