Not starting, drove day before

Fuses do not cause intermittent problems. When they fail, they're done. Since the no-crank is affected by playing with the shift lever, that is the obvious place to look. The neutral safety switch has to be in the "park" or "neutral" position for the starter system to work. An anchor at one end of the cable could be loose or broken. The cable could be out of adjustment, etc. Try shifting to neutral to see if the starter will work.

What do you mean by "problems with gear shift not going into park all the way". Do you mean you can't move the shift lever into park unless you push really hard? Do you mean you shift into park but the car still rolls freely? Do you mean you have trouble getting the gear you selected and you have to move the shift lever around a little?