how can i see if apple care is on my device if i can't turn my phone on?

You may use a web browser to get the Serial Number and the IMEI Number. You cannot track using the IMEI number. but you may need it so keep it handy

Log in to https://appleid.apple.com with your Apple ID credentials. All your devices will be listed there. Click on any to get the details.

Check your Apple warranty status. Enter a serial number to review your eligibility for support and extended coverage.

Check Your Service and Support Coverage - Apple Support