The HDMI port is soldered onto the motherboard so I agree with Scottray, if you want to use the HDMI port you are going to have to replace the motherboard. I just saw a motherboard for that model on eBay for $120.
You plug this into the HDMI input on the TV and also into the USB port on the TV. If your laptop supports wireless displays you will be able to broadcast your screen to the TV. On my Windows 10 laptop, if I click on the Action Center button (bottom right of screen) and then click connect it starts searching for wireless display adapters. If yours has this then it supports that feature.