Like they said, DON"T mix the old sand with the new.
When you transfer the old sand bed to a new tank, the pretty delicate organisms that were in the old bed will be mixed up. Those critters who lived in certain parts/layers of the sandbed will be disturbed/cut-up and most will probably die. Then, in your new tank, the dead organisms will pollute it and cause it to crash. You will have nothing but problems. Voice of experience.
So your live rock that you have rescued will help filter and re-seed your new tank. If you want a new sandbed, put in freshly rinsed new sand, and seed that with a cup or two of a buddy's sandbed. Believe me, it's cheaper in the long run. You won't have epic battles that'll take years to resolve.
You will have to go through a small cycle regardless of how you transferred your livestock. Just be vigilant and be ready to do lots of water changes.
Less trouble than to have everything die off due to sand bed collapsing on you, trust us.
Good luck.