if the TV only has HDMI and the computer only has 15pin VGA you need one of these. http://www.newegg.com/Product/Product.aspx?Item=9SIA1NV0H82039
Your challenge is that the computer only puts out analog video in the form of VGA. You need a converter to convert that analog signal to digital for HDMI.
Are you sure the laptop does not have HDMI or Display Port?
If the TV has a 15 pin VGA I would just use that. The quality is very good at 1920x1080@60hz.