Can my notebook be displayed on my TV?

It is a Lenovo Thinkpad T410 with a Broken Screen. Maybe some cable to hook up to the TV?

Maybe.
What ports does your laptop have? Does it have an HDMI or VGA output?
What ports does your TV have? Does it have an HDMI or VGA input?

Certainly possible, you will need to update your post with details of the connectors on the TV.

Your laptop has a VGA port,
if your TV has a VGA port use a straight VGA-VGA cable
If your TV has a DVI port use a straight VGA-VGA cable and a VGA-DVI adapter
If your TV has an HDMI port you will need a VGA-HDMI converter box (VGA-HDMI cables are available but they never work)
If you TV has anything else update your post

Once you have the correct cable/converter there will be a function key combo on the laptop, hold down the Fn Key bottom left of keyboard, look along the row of function keys for a monitor symbol, tap it and it should direct the output to the monitor. Check the monitor is set to the correct input

HDMI is the usual or a vga / hdmi adaptor but for that you might need a separate sound cable