Ugh, been there - except mine was the kitchen sink flooding at 11pm before Thanksgiving. Absolute chaos. The "let me just Google a fix real quick" spiral is so real, and yeah it almost always makes things worse.
For the humming-but-nothing situation, that's usually the motor or pump trying to run but something's blocking or fried - definitely past the DIY point. A neighbor pointed me to Local Appliance Repair Company in Denver Metro - High City Appliance and the tech actually explained what went wrong instead of just handing me a bill. Felt fair, not like they were inventing problems. Might be worth a call before you spend more on parts guessing!