You need to have your bios at 0904 or greater to support the i7-4790: http://www.asus.com/us/Motherboards/H87ME/HelpDesk_CPU/
Using your i5-4440, update the bios for your board. Then install the i7-4790.
You cannot install the z97 chipset. Your chipset cannot be changed from the H87 as it is integrated into the motherboard.
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