Is there a way of leaving your headphone jack in your tv and switching to the tv speakers without taking the headphone jack out from the tv?
The headphone jack switches the speakers off automatically on most televisions, so you won't be able to disable this function without doing electrical surgery on your television.
For sound cards: Check the back of the computer. If you have some headphone-looking ports in a rectangular shaped metal cutout back there (and there are more than one) put the speakers in the green port. For Computers without sound cards: If you don't have one, look for the mouse and keyboard ports. Close to those, there should be around 3 headphone-looking ports, put it in the green one. Also, it would greatly help if…
That depends on whether or not your computer has speakers. If it does, then unplug your headphones, plug in the speakers, and make sure your volume is turned up. If you don't have speakers, then there is no way to do have sound without headphones other than to buy speakers. Most desktops have speakers built in to them, though.