Hi @edthomas25 ,
If the case is bent out of shape check that all the internal cable connections e.g. battery, IO board etc are secure as moving the lid may cause movement in a loose connection. Also check for any obvious damage around the power button area.
Looking at the [https://download.lenovo.com/consumer/mobiles_pub/yoga_c740_series_hmm.pdf|hardware maintenance manual] for the laptop, the power button is on the IO board ([https://www.ebay.com/itm/5C50S24992-Lenovo-USB-IO-Board-W-FFC-Cable-For-Yoga-C740-15IML-Notebook-Series-/274623419731|part #5C50S24992] - supplier example only to show the part), which connects to the systemboard.
Hopefully this is of some help.