If you can not upgrade to High Sierra, then upgrade to Sierra. Again use this answer to upgrade to High Sierra.This step may not be necessary, since installing Sierra and/or High Sierra will also upgrade the firmware. Open the Install OS X El Capitan application to upgrade to OS X El Capitan 10.11.If you can not create the USB installer, then skip this step. This USB drive could be used to do a clean install, if something goes wrong. (Optional) You probably should try to create an USB El Capitan installer by following these instructions.

Put the InstallMacOSX.dmg file in the Trash and empty the Trash.

From the Finder application, eject the Install OS X volume.

The Install OS X El Capitan application will take 6.22 GB of space. If not, then open the InstallMacOSX.dmg file and then open the Install OS X application.

Run the Install OS X application to create the Install OS X El Capitan application in the Applications folder.

Click on the OS X El Capitan 10.11 link given in this answer to download the file InstallMacOSX.dmg.

If you can not use an USB port, then use the internet to transfer files to another computer.

(Although, you should be able to use your USB ports if they are not broken.) One path could take which would not use any USB ports are as follows. The pre-installed OS X was Snow Leopard (OS X 10.6.1 or OS X 10.6.3), so you would not be able to use an USB installer created from the original Snow Leopard (OS X 10.6) DVD. Regardless of whether your Mac is a 2009 or 2010 year model, the maximum macOS that can be installed is High Sierra (macOS 10.13.6). There is also the Apple websites How to get old versions of macOS and How to create a bootable installer for macOS. It would be very remiss of me not to mention Tetsujin's answer to the question How can I download an older version of OS X/macOS? According to this Apple website, this update would give a MacBook (13-inch, Mid 2010) the ability to use Internet Recovery and thus an alternate method of reinstalling OS X/macOS.

There appears to be an update to 0E for the MacBook (Mid 2010), which requires at least Mac OS X 10.7.2 to install. A 2009 Macbook would have a ID of MacBook6,1, but you state a ID of MacBook7,1, which is a MacBook (13-inch, Mid 2010).

A search for A1342 by results in the following Macs:

Osx boot from usb