Only the DVI-I port no HDMI port, can use Applr TV?
My TV model is Sharp TU-324GH, (http://www.go-gddq.com/down/2012-01/12011407508070.pdf) which only display 1080i and no HDMI in port, may I use Apple TV?
Apple TV (3rd generation), iOS 7.0.4
The only supported method is HDMI, there is no guarantee with others. If it does work you may have issues with protected content (ie iTunes, Netflix).
Also, Apple TV supports 1080P, but not 1080i