I just had the same exact thing happen to me. I use GoDaddy as well. I had to manually remove the garbage from the beginning of dozens of PHP files and then re-install a lot of plug-ins.
Here’s what was at the beginning of each file:
<?php $byslzxrsoq = '5c%x782f . . .
I just ran into the same problem this morning.
In an effort to be tidy and document my custom code, I added a line containing comments just before some custom PHP in my child-theme’s functions.php file. Once I put the comments inside of the PHP tags, the error went away.
Hope that helps everyone else too!