I opened up my computer to install a new harddrive. After putting it back together, it won t output a display to my TV anymore. Why?

As I understand as you describe your monitor is receiving no input. Not just a blank screen that may indicate that the computer cant find the os. If it is getting no signal that you need to instigate the graphics output and the monitor. There is nothing that you would normally come across on the hard drive said that would cause someone to accidentally disconnect something graphics. There may be a power cable to your graphics card if it is is not onboard. Other than that there is just it's HDMI cable.

did you REPLACE the old hard drive? in that case, you need to reinstall Windows.

if you simply added ANOTHER hard drive, then that is not the problem.

be sure the graphics card did not have an external power plug (some do).

also, be sure you plugged the monitor into the proper output on the card. if you are using a TV, keep in mind, some cards will output to the OTHER ports by default, then output to HDMI once Windows loads. turn on your computer and wait a full 5 minutes, and listen for the Windows startup sound. if you hear it but do not SEE anything, be sure the card is snug in the slot. if it is, you may need a new card...or maybe your TV's port is damaged...

Did you connect the monitor to the graphics card or the on-board graphics card mistake?