How many IR LEDs needed to get accurate remote control signals around room
One. It works very well with just one led.

You need one led, not more. If it is not working with one led, then you have different problems. The TV receiver is usually an integrated receiver such as http://www.vishay.com/docs/82491/tsop382.pdf It is quite sensitive, contains an AGC circuit to control the amplification, and works very well even if the infraled light is bouncing off from some walls.

There are two ways to reduce the distance (what you may also see):


using a wrong modulation frequency. Although a 38KHz receiver can receive 40KHz signal too, the distance will be much smaller.
using wrong light power. It is important that one infrared pulse at 38Khz is a clean pulse, with a 50% pulse width. If you have this many leds, your power supply can easily have glitches. You can see that on scope.


If you show the driving circuit and tell about the power supply, there is a chance we can reveal more potential problems.