how do i fix my iMac serial number El Capitan corrupted
i upgraded from Yosemite to El Capitan .. then discovered i could not sign into iTunes or into the AppStore with my apple id .. i validated my apple id but am only able to sign into iCloud .. El Capitan changed my iMac [model iMac7,1 ; Boot ROM ver IM71.007A.B03 ; SMC ver 1.20f4 ] system serial number from 11 characters to 10 characters , it lost the 6th number. I checked my other external bootable drives running Snow Leopard, Mountain Lion, and Yosemite and each read/showed the changed serial number from the firmware in the logic board. Apple Care Telephone Support has indicated the resolution is to simply 'reformat my internal hard drive' and then 'restore the El Capitan software backed up using Time Machine'.
Has anyone done the above and successfully changed their corrupted serial number in their iMac??
Two years ago the Apple Store replaced my logic board. If the board were incorrectly replaced could the serial number have been changed, yet working okay with Maverick and Yosemite but not with El Capitan ??
Any help would be greatly appreciated. Thanks.
iMac (20-inch Mid 2007)