Maybe the tank is about empty. IF someone (constuction workers or someone on lower level than you or turned off main supply line but left some other valve open and drained all the water out it will take couple minutes to fill up the water heater and they possibley burned out elements also from no water in tank. Or check the areator on the faucet they get full of lime and deposits where the water won't come out either If its spitting and such sounds like bunch of air in line too me though.
Need more input.
How long did you leave faucet on ??
swamp
edit: re read post and if its been like that all week then tank would have water so I would guess deposits in pipes and valves. I cleaned out my water heater last year and I got about a gallon of lime and junk out of it and it's only 4 years old.