"car turns over, but wont start"

first off, let me say i know how often you must get questions like this from people who dont know about cars. im a snowboarder/skateboarder.. in snow/skate world i am the equivalent of an automotive expert here, and we get people who know nothing about it all the time just like you.

anyway, my trouble is as follows.

ive got a 93 subaru legacy L wagon. in the past 4 days its been really cold, about 5 degrees F, and with wind chill i believe it reached down to 15 below at times, or overnight. as soon as it started to be this cold, my car took longer to actually start in the mornings, but that was the only time it took longer (its never done it before this drastic cold spell), and every other time during the day that i started it, its been fine. today, it just didnt start.

the only thing thats happened besides the cold since its been doing this, is my battery died and i replaced it. i know it was dead, because it was already old, and it only clicked when i tried to start the car. i didnt touch anything besiedes the two cables to connect it. as soon as i had the new one in, the car started right up.

i went to start it this morning, and it would turn over as quick as usual, and didnt sound any different, but it wouldnt start. sometimes i can hear a rumble in the engine like its JUST about to start, but never quite gets there. ive been troubleshooting, and ruled out anything to do with the alternator/battery/starter (i think).. the only thing i have left is that maybe its not getting a good enough spark, or none at all, and maybe thats caused by the computers sensors not working properly and giving it the wrong mixture or something? or maybe something in the spark-related area is off. im not sure. my battery is brand new, ive got plenty of fuel, and i cant think of anything else.

its very sudden, so im pretty confused, not to mention im no car expert at all.

one other thing is that as long as ive had the car (its only been a few months so far), its been weird with acceleration sometimes. its like it wont fully kick into gear when i start moving from a dead stop, and if that happens, it tends to also be, while accelerating, kind of jerky until i get up to speed. im not sure why that is, but maybe it has something to do with whats happening now.

sorry for the length, and for my lack of knowledge, but thats why im here. im trying to avoid going to a shop as much as possible because they love to suck money from people.

if you have any ideas, especially in detail, theyre greatly appreciated. and talk to me like im stupid, because im not gonna know most of the words and terms.

thanks.

also, what about oils? ive been reading a lot about all this cold weather stuff, and the oil viscosity keeps coming up. i think ive got 10w-40, which ive read is a warmer weather kind of thing, and that i should be using 5w-30 or something. do you think that 10w-40 could be affected enough by temps in the 0-10F range to cause the engine to not start, but it would still crank and get close to starting?

im really focused on the cold, because thats when starting my engine started to be different.