I live in Duluth, MN.  We've had brutally cold weather on and off for the last month or so.  I was experiencing hard starts on some of the coldest mornings and eventually, this week, it wouldn't start.  My dash and interior lights were functional and it cranked but didn't start.  I hooked up jumper cables and let it juice up for about 20 minutes.  It started and I drove it for 30 minutes.  When I turned it off and attempted to restart it, it cranked but didn't start. 
  
I replaced the battery and cleaned the terminals. 
  
Same result.  It would crank, but wouldn't start.  It did start once with the new battery, but only when I fully depressed the gas pedal on a few attempts.  It idled fine, but died when I revved the engine.  After that, it would crank but not start. 
  
Any suggestions? 
  
Thank you in advance...