The message you mentioned intitially ("insert a boot drive and press any button to continue") indicates the SSD has issues being detected.. if you updated to Windows 10 which should have replaced the Windows bootloader and the issue remains, that indicates the problem is the SSD partition table, a Windows upgrade doesn't repair a partition table, a format has to be done to achieve it, or you could try repairing it with a Partition Manager
I typed repairing a GPT partition table, to find solutions so I hope it's not MBR... try Minitool Partition Wizard, if it doesn't help, try AESEUS Partition Manager, AOMEI Partition Assistant. If none can do the repair, you will have to backup your data on the HDD and format the SSD to start with a new partition table and install a fresh copy of Windows... but retrieve the Windows Product Key before anything else, to use it on the new installation.. (if it gets to that).
You can download a Windows 7-8-10 ISO from this Microsoft page (don't need a Product Key to download) to build a Windows DVD or USB installer.
https://www.microsoft.com/en-us/software-download/windows10ISO
Product Key Finder
https://www.magicaljellybean.com/keyfinder/
Partition table repair options (software downloads & manual repair instructions)
https://www.google.com/search?client=opera&q=how+to+repair+gpt+partition+table+from+Windows&sourceid=opera&ie=UTF-8&oe=UTF-8
Slightly different results/options
https://www.google.com/search?client=opera&q=how+to+repair+gpt+partition+table+from+Windows&sourceid=opera&ie=UTF-8&oe=UTF-8#q=repair+gpt+partition+table+from+Windows
GPT fdisk (GPT/MBR Partition table repair)
https://sourceforge.net/projects/gptfdisk/
GPT fdisk Tutorial
http://www.rodsbooks.com/gdisk/
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