Don't try burning a DVD of the installer. Almost certain route to failure.
Do you have a USB flash drive around, 16gb or larger?
THAT'S what you need to create a bootable installer.
You also need "Diskmaker X" to create the installer.
Get it here:
diskmakerx.com
By the way, I would recommend 10.12 "Low Sierra" over High Sierra.
But in any case, once you've downloaded the OS installer, use THE PROPER VERSION of DiskMaker X to create the bootable flash drive.
Can you get this done? See next step.
One other thing:
Once you have the bootable flash drive, and you're ready to give it a try, DO THIS FIRST:
a. DISCONNECT the Mac from the net (remove the ethernet cable)
b. Go to the "date and time" preference pane
c. UNCHECK the provision to "set date and time automatically"
d. Now, SET BACK the clock to December 1, 2018.
e. Close date and time and now reboot from the flash drive.
See if this works. Apple (for reasons of its own) has "deprecated" the certificate on older installers, and they won't run UNLESS you "set back the clock" to a date before Apple's cutoff date.