The X: drive is not where Windows is installed. X: is the RAMDisk that Windows setup and recovery loads your Windows installation media into so it can be accessed quicker from the RAM instead of from the CD/DVD/USB drive.
I am concerned about the 4 GB drive being the only drive that shows up in Diskpart -> List Disk; you should be able to see your 64 GB SSD through Diskpart if it is working properly.
Can you provide a picture of the Diskpart -> List Disk command output? Use a digital camera without the flash on to take the picture.
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