First I usually find the user is trying to mirror the screen to the TV. You left out the TV model so I can't check if it's some 720p TV which would not take the resolutions you listed.
Next time extend the Windows display so you have two displays. One will be the laptop screen and the second the external TV.
Plenty of tutorials on the web about extending the Windows Desktop so I pause here.
I used to use a HDMI cable all the time to stream from my previous laptop (Samsung) to TV (Samsung). Now I've bought a new laptop (Dell Inspiron) but when connecting it to the TV with the HDMI cable a message appears on the TV screen "resolution mode not supported, change the resolution". The default resolution of the new laptop is 1920x1080, when I saw the message I changed it to the lowest possible one (800x600) and picture appeared on the TV screen briefly but then stopped working and I've been unable to get it to work again even though I've tried the majority of available resolutions, including one that used to work on my previous laptop (1366x768 refresh rate 59p or 60p Hz). Is there anything else I could try, is there any solution?