Been there. Done that.
It may be the LT is toast. But. I have this aversion to tossing something like this when there is a chance I can revive it. It all points to something resident in the Lenovo Care to me. BIOS recognizes both the HDD and the USB DVD and "sees" their names. I have the boot sequence set for USB and I can also hit F12 and choose it there when booting.
If you have a decent sized USB flash drive, just make a bootable version of your Mint ISO.