Dishwasher not draining

It’s an 11 year old Kenmore dishwasher, Mod. 665.1552. It goes through the whole cycle, not a drop of overflow on the floor, but after the cycle the bottom is filled with water. The sink drains perfectly(no garbage disposal). I disconnected the drain hose and attached it to the shop vac. to hopefully suck out any junk. No water or junk came out. I read something about the float inside the machine being dirty or faulty. I gave it a slight tug but it didn’t come off. Is there a way to check/clean it? I’m really not into pulling it out and trying to troubleshoot it. I’m wondering if I should even call for service for this old machine that only cost $350.