Something just doesn't sound right about that, it's relatively remote that both lines coming to your pump would plug up at the same time, could the problem be the pump itself?
Maybe the shop vac isn't strong enough to force air through the length of line you're trying to do......
Have you tested to see if the rinse or whirlpool setting will allow you to push water - whirlpool essentially bypasses the filter, and rinse completely bypasses the filter and anything beyond that...
Could also be that the feed to the filter is clogged - if it can't push water, it also can't pull water from the pool - although this does not explain the apparent blockage that's stopping water form flowing back to the pool.

When you took the valve out, did you try sticking a fish tape or drain auger down either pipe on the left and right of the valve to see if there's an obstruction relatively close to the valve?

I think at this point, your best bet would be using compressed air to try and blow it out, don't go higher than 40lbs pressure though, you may break a pipe with more.