Rejected transaction What means this: "Transaction rejected by our node. Reason: Non-canonical signature: High S Value". It came after trying to send BTC to my new Qt-wallet from old synchronised wallet (version 0.8), which was restored to status about 1 month ago by copying backup wallet.dat file.
There are two ways to create signatures for transactions. One uses a High S Value and the other a Low S Value.  Since the signature can be malleated by third parties (also see transaction-malleability) to switch the High S to Low S and vice versa, and that changes the transaction id, High S Values have been deprecated for several versions.

You could either malleate the transaction's signature to Low S and republish it, or you could just import the wallet.dat into the new Bitcoin-Qt that you're trying to send the funds to anyway.

Be sure to create a backup of the new wallet.dat before you import the old.