MacOS – Will ‘Internet Recovery’ necessarily erase the hard drive

1. Connect the external drive or device to the Mac
2. Reboot the Mac and after the startup chime hold down the OPTION key during boot until you see the boot selection menu
3. Click the external volume to boot from it

After this steps, you will find that external drives typically are shown with an orange icon, with their interface printed on the icon itself. Similarly, CD’s and DVD’s are shown with a disc icon. In this screen shot example, the right-most orange boot drive is a USB flash disk.

This works for quite literally any boot volume, whether it’s an external USB drive of any sort, a Thunderbolt hard drive, boot DVD, CD, the Recovery partition, even in dual-boot environments with other versions of OS X, or a Linux or a Windows partition with Boot Camp, if it’s bootable and connected to the Mac it will be visible at this boot manager.

Though boot DVD’s and CD’s will be visible through the aforementioned boot manager, you can also start the Mac directly to DVD or a connected disc by holding down the “D” key during restart after you hear the chime. This is fairly uncommon these days, but it was the primary method of accessing recovery partitions before OS X became a download from the App Store, and before USB installer drives became more common.

Additionally, Macs with recovery partitions can be start directly into Recovery HD by holding down Command+R during system start.

Though recovery and discs can be booted with their own commands, it’s ultimately easier to just remember the Option key method since it is a single key and because it’s universal. The only exception is with target disk mode, which requires a different sequence to use.

Since only one drive gives you a flashing ? when mounted internally, you've pretty much ruled out hardware failure of the controller and the cabling.

I would first try booting into the start up manager by holding the option key with the problematic drive on the internal bus. The ? can come up when the startup disk settings in NVRAM don't match the drive, but if any drive connected is bootable, it should show when you boot with option held down.

Your next step after making sure it's not startup disk settings would be to erase that drive entirely and try reinstalling OS X onto it. You could flip a coin and decide to do the installation internally or externally.