If MSFT won't let you, these googledrive mirrors are apparently active (I pasted the googledrive adress into a browser, and the link I pasted started the download popup question for windows 7, sp1, 64bit home premium, and when I told it to download it began downloading... )
the links to digitalriver ISO downloads were inactivated by MSFT, but these googledrive copies could help you.
http://hasibul.info/blog/2015/04/12/...7-iso-updated/
This will only work if you recorded the windows 7 key (or have the sticker with the key)
Vaio esupport can provide the drivers.
http://esupport.sony.com/US/perl/sel...ODTYPE=1,24,72
One more thought I had was that the broken internal DVD-drive could trigger errors during setup.
You may want to pull it out.
This is usually possible by removing just one screw and a sliding a locking slider somewhere in that vaio, but you may have to look "under the hood" (remove more screws) to see which hook or screw secures the internal DVD to chassis.
Get the Vaio esupport chipset drivers, these should have the hard disk controller in them. Get the others too, just in case.