2003 Corolla dead and won't jump start

Hello,

I have a 2003 Toyota Corolla that died on me.  I turned the car off when I
got home and noticed my powerlocks weren't working.  I tried to turn on my
radio and re-start the car but no luck.  I have a like-new battery in it, (got it
a month ago) and I cleaned my battery terminals and cables.  

I also swapped out the "main fuse" with the spare one that came with my
corolla.  I tried to jump it again and it worked.  I drove the car for a few
more days and it died on me while I was driving.  No power again and this
time it won't jump start.  I don't know what's going on, I thought it was the
alternator but my neighbor (he knows more than I do so I asked him for
help) said it's not related to the alternator.  He said it's computer/electrical
failure.  We did check the main fuse and it's still in good condition.  Any
thing I might be missing?  if there's any info let me know I can provide.  
Thanks