I would bet you drained the transmission oil and not the engine oil. It is a pretty common mistake.
How much oil did you add when you where done. is the oil level on the oil dipstick now reading overfilled? Is there any fluid on the transmission dipstick?
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Did you change the engine oil or the transmission oil (fluid)?
If you changed the engine oil, I can't see any reason for an apparent transmission malfunction.
If you changed the transmission oil (fluid) and you didn't put enough back in, then it will not have enough to engage and cause movement.
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