When I turn the key all of the electronics come on and there's a click and a whirring sound

Yesterday morning I hopped in my 96 Camry to drive over to my parents'. It started with no issues, but I only got about a block before it suddenly died. I tried to restart it, but the engine wouldn't turn over. I pushed it over to the side of the road, and popped the hood. I noticed a sizeable amount of oil that had apparently leaked from the oil filter. I checked the oil level and it seemed to be low. I wondered if the level was too low and the engine might have seized, but the oil pressure light has not been on at all.

This morning I went back to try the car again. When I turn the key all of the electronics come on, and there's a click and a whirring sound (which I'm guessing is the starter motor trying to turn the engine over), but the engine doesn't engage. I checked the oil again, and it shows a decent level (about 2/3 on the dipstick).