Q: How do I transfer data from a MacBook Pro (2009-does not want to open) to a MacBook Air (2015)?

If the MacBook Pro won't boot, then there's no way to transfer data to the MB Air.

You restore the data to the new system from the backup you made of your old one... Or, you could get your old one fixed, provided the the hard drive is not the component that failed... taking your data with it. Or, you have someone physically remove the hard drive from the old machine (provided it actually still works) and put it into an external enclosure you can then plug into the new machine and copy the data.

Target disk mode may work if your 2009 Mac can boot into that…

How to use and troubleshoot FireWire target disk mode - Apple Support

You will need appropriate cables to connect it to the new Mac, probably Firewire to Thunderbolt via adaptors.

The old disk should mount on the new Mac.

You can test it without the cable - you should see a firewire logo screensaver if it works, press the power button to shutdown safely.