arrastrar

The everyday verb for dragging something along the ground — a chair, a heavy bag — and, figuratively, for carrying a burden over time (arrastrar una deuda/un problema desde hace años, to have been dragging along a debt/problem for years).

• Arrastró la maleta hasta la habitación porque no tenía ruedas. — He dragged the suitcase to the room because it had no wheels.
• Arrastra ese problema de espalda desde el accidente. — He's been dragging that back problem along since the accident.
• El río arrastraba ramas y piedras tras la tormenta. — The river was carrying/dragging branches and stones along after the storm.

Missing the figurative, ongoing sense — arrastrar un problema/una deuda doesn't mean physically pulling anything, it means having carried it, unresolved, for a long time.