My car has been doing a similar thing the last two mornings. I had to leave it outside for the first time since it became a daily driver. The temps got down into the 40's (coldest its been this year) and it had a little problem staying running for the first 30-50 seconds. It also took a few more revolutions of the starter for it to actualy fire up.
Completely unreleated (or maybe not) the power steering belt came off of the pulley on the way home from work right after I got off of the freeway.
I will edit later and add link to new thread started about the issues. I dont want to Hi-jack.
Kid, (PimpiNJ253) dont sell your car, you will learn an invaluable amount of info about cars in general solving the problems you encounter with this car. This community is huge and the majority of them KNOW whats up when it comes to solving REAL problems. Its not a bad car and all cars have some personality querks. And Just see if you can find a forum for Maximas where the percentage of members have actually WORKED on their cars and SOLVED problems they have encountered. My guess is the majority of the members will have a Stereo component of some sort listed near the top of their mods.
Go to Napa ask to see their Weather pack catalog order just the Pins and sockets 11-14 cents a piece. Go to any junk yard with a GM car in it. Use wire cutters to clip off any 4 wire connector (get the matching male and female connectors) take your connector assembly and your 4 pins and 4 sockets, use the yellow pages to find an automotive electrical specialist. Call and ask if they have the pinout tools for weather pack connectors, if they say yes drive straight there. DONT go to the counter, Walk straight thru the garage bay doors (preferably when the boss isnt looking) ask any mechanic who the electrical guru is. Walk straight to him show him the new parts in your hand and ask if he can install these (tell him they are right on top of the motor) after work. If your nice he might do it for free. If he says it will be 20 bucks, go buy the pinout tools and do it yourself. Once you remove the terminal from the socket you will see exactly what you have to do. All you need is a cheep wire stripper/crimper. The electrical dude should have the real deal GM tools for this whole job and it shouldnt take more than 10 minutes.
Without this info you are correct not to try to solve this problem the car stereo way. Dont solder anything unless you have to.
Good luck