The Cleric casts silence on the burly fighter...The burly fighter (quietly) charges up to the enemy caster who has Spell Resistance. Does the enemy caster get to try his SR against the silence spell, or can he just not cast verbal spells unless he moves out of the radius of the silence?
No, only the target of the silence spell can use SR or saves to negate the spell. Creatures in the radius of a silence spell do not get to use their SR or make saves to avoid it.