My car starts, but as soon as I shift into Drive or Reverse, it doesn't move. The only codes I got were P0010 and P0013.
The transmission in your Equinox (the 4L60E) is common - I replaced one recently. I suggest starting by checking your transmission fluid level: Start your vehicle, let it warm up, and with a rag, pull up the transmission dipstick tube from the rear right side of the engine compartment; verify the fluid level by cleaning off the dipstick, reinserting it, and checking again. Your car's service manual should tell you what the fluid level should be. If your fluid is low, then add Dextron 6 fluid.
The codes are not likely related to the problem you described; they are related to camshaft position codes, which can include anything from replacing a timing chain, to faulty timing solenoids. Sometimes a sludge build-up on the solenoids can cause the Check Engine Light codes.
I recommend having a certified mobile mechanic, such as one from YourMechanic, come out to your home or office to run a diagnostic inspection of your Check Engine Light illumination, and recommend the best path to repair.
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