It may be too late, but pull the battery and leave the phone and the battery alone for 24 hours. (If you can, now is the time for the "rice trick" - put the phone and battery in a bag or jar of uncooked white (not instant) rice while they sit - the warmer air inside is going to cause condensation, and the rice will absorb a lot of that. If you have a pound or two of silica gel, even better.)
After 24 hours, put the battery back in the phone and see if it turns on. If it does, turn it off, plug in the charger and leave it alone (still in the rice) for another 24 hours.)
After that it should be back to normal, although the battery may have lost a few months of life. Charging a lithium battery when it's below freezing (32F) is bad for it. You can
discharge the battery at down to -4F, but that will reduce the life a little bit.
If the battery is shot, S4 batteries are about $10 (
Robot Check).
The screen is another matter. An LCD screen normally shouldn't be allowed to reach a temperature lower than -4F. (Depending on the "liquid" part of "liquid crystal", the liquid can freeze and the crystals can puncture the film, destroying the screen.) Operating down at 25F? It may not look great, but it shouldn't cause damage. (The screen will lag when it's cold, and lag pretty badly when it's very cold.)
BTW, "insert the battery. When I do, the phone vibrates, I see the black samsung galaxy s4 screen for probably 1.5 seconds then it goes blank" usually means a wet phone. It's probably too late, but you could try alcohol.
Oh, no! My Phone got Wet!
The rule of thumb is that if the temperature is too low or too high for you to be comfortable in a short sleeved shirt, it's too low or too high for the phone.
There are two reasons to not leave a phone in a car. 1) Temperature - the 150F or more in a car parked in the sun in the summer (yes, in NY - I grew up in NYC and raised many blisters as a kid touching the railing on the boardwalk in the summer) can destroy both the phone and the battery, it's not just the winter that's a problem, and 2) the very real possibility of coming back to a car with a broken window and no cellphone. Look on eBay - you'll see a lot of "bad IMEI" or "bad ESN" phones for sale. That doesn't mean the IMEI or ESN "broke", it means that the owner reported the phone stolen.