Dead Deodar Cedar?

Hi everyone,
It's been a while since I've posted.

About two months ago our water meter had broke and my trees went without water for about two weeks. Half of my collection had died but the other half is still going. About 40+ trees were lost during this drought. I am moving to a new location in a weeks time, and I'm checking all the remaining trees (some which I thought were going to pull through, apparently didn't make it) I am however, two minded about the life (or death) about my Deodar Cedar. Around a month ago, I would cut off an overgrown branch and it was still green. The tree has discolored since then, so I decided to properly check if its still alive by chopping the tree down every 10cm or so. (obviously starting with a very small tip of the tree) Now I have cut it down to about 8cm roughly. There is no green to be seen at all, but the bark still has a sticky sap. My question is, is the tree dead? Is there perhaps hope? I know looking for green would be the main component in checking if a tree is alive, but I have not experienced sticky sap from a dead/dying tree, since this was my first and only Deodar Cedar.

Anyone with experience with this, please tell me if its dead or not(if possible). And yes I know from the other information I have given, the tree would be dead. But it is the sticky sap I am wondering about, which could potentially mean its got some chance?

Regards,
Shayn