First of all, stop replacing parts until you find the problem. You could have hired a
mechanic to trouble shoot it for you for the price you spent on unneeded parts.
Scan the car for trouble codes. They may be gone due to the battery
replacement, but they might still be there. Check all the various grounds on the
car. There are several. Find them and clean and tighten them. Proper grounds
are extremely important on modern cars. Check all fuses and relays in the fuse
panels to make they are all in place and working. It sounds electrical to me. After
you've done all that you still may need the services of a technician who is
experienced with trouble shooting automotive electrical systems. Good luck.