Well, after a week of waiting the parts finally arrived. With some help, I desoldered the old Flyback Transformer, C1, Q3, and CR1. I installed the new parts from Digikey, and this is the final result after some screen and voltage adjustments:



The Old Parts:



There also used to be a faint clicking sound when the ? Floppy Disk screen would appear, but there isn't anymore. The new flyback transformer appears to be working perfectly, and I have had no screen problems since. The speaker works perfectly.