Hi,
Here’s a link to the [https://download.lenovo.com/consumer/mobiles_pub/lenovo_z_p_series_hmm_v1.0.pdf|service manual] for your laptop, taken from this [https://support.lenovo.com/au/en/solutions/ht101562|webpage - IdeaPad P500 touch] .
Scroll to p.33 to view the procedure to remove/replace the keyboard.
Use the procedure to inspect the keyboard cable connection to the motherboard to determine if it is OK or not.
If you need to replace the keyboard, on p106-109 you will find the part numbers for the type and country specific keyboards available for your model.
If you search online using the appropriate part number ''only'' in the search box of your browser, you’ll get results for suppliers of the part. Usually the part number is to be found on the back of the keyboard if you wish to verify that you have the correct part number