Hard to tell from the photo of F901, but it might be blown. Check it. If it is, you most certainally need a flyback and a HOT.
Speaking of flyback, that picture you posted is a neckboard, not a flyback. The flyback is the grey block with two knobs and the thick wire coming out of it.
As for the caps - yeah, those are pretty bad looking, you're definitely due to recap that. But usually they only cause picture distortion, foldover, sync problems, etc. The right bad cap can cause a dead monitor, but usually on a G07 it's the flyback that goes.
Take a look at the flyback, see if there are any cracks or burn marks on it. And check the little fuse (F901) to see if it's open.
You're probably going to need a flyback and HOT, a couple fuses, and do the caps while you've got the chassis out. Bob Roberts has a G07 "Repair Kit" that contains the flyback, HOT, both fuses, and all the caps. IIRC it's like $28.
-Ian