Either the water table is genuinely high, or the pump is short-cycling because the check valve is failing and discharged water is running back into the basin. A pump running with no rain in days points at the check valve or a stuck float.
More detail
Constant running is a symptom with a short differential, and it is worth resolving because a pump that cycles unnecessarily burns out early. The most common cause of running with no rain is a failed check valve. The check valve sits on the discharge line and stops water in the pipe from falling back into the basin when the pump shuts off. When it fails, the same water drains back, refills the basin, and triggers the pump again seconds later. The tell is a rapid on-off-on cycle every minute or two. It is an inexpensive part. A stuck or misadjusted float produces the same pattern by never telling the pump to stop, or by sitting too low so the pump starts on a nearly empty basin. Floats also snag on the basin wall or on the discharge pipe. Genuinely continuous running with steady inflow means groundwater, and that is not a pump problem. A high water table after sustained rain, a spring under the house, or a downspout discharging next to the foundation all deliver real water. The downspout case is worth checking first because it is free to fix: a disconnected or short downspout can put hundreds of gallons directly against the wall in one storm. On the other failure, a pump that never runs at all: test it by pouring a bucket of water into the basin. If it does not start, check the breaker and the GFCI first, then the float, then the pump. Service life is three to seven years of typical duty and shorter for a pump that has been short-cycling. The failure that causes damage is almost always coincident with a storm-related power outage, which is the argument for a battery backup rather than just a newer pump.