Yah, unless you have a clog in the block or a collapsed hose, something weird like that. You're clearly not getting much flow if the system is full but the lower hose is cold. I've seen hoses delaminate and collapse on the inside without looking squashed on the outside, usually from rusted-out spreader springs. If you haven't checked them you should, especially if they're old. It's messy, but you can check the pump by pulling the stat and sticking the lower hose in a bucket of water. You can also check the stat by disconnecting the upper hose and see if it goes from a trickle to a gusher when the engine warms up.