Okay, let's start out with a clarification. LED replacements for fluorescent bulbs do not contain phosphorus. Fluorescent bulbs work by running high voltage through mercury gas, which produces ultraviolet light. Of course, that doesn't help light up your house, so they coat the inside of the glass with phosphorous, which glows white when exposed to ultraviolet light.
LED bulbs don't need that conversion, so there's no need for the phosphorous.
Regarding your actual problem, fluorescent fixtures are pretty simple devices. They really only have two parts; a ballast that boosts the line voltage up to anywhere from 300 to 900 volts to start the current flow in the tube, then drops back down to anywhere from 100 to 175 volts once the current flow has started.
So really, since you've replaced your fluorescent bulbs with LEDs, the only part left that could be giving you trouble is the ballast.
At this point, assuming you have a bad ballast, you have two options. First, you can try and locate a replacement ballast, which is probably feasible; places like Home Depot do sell them.
The other choice is to eliminate the ballast completely. LED replacement bulbs come in two styles; ones that are compatible with a ballast, and ones that simply run on straight line voltage. The second style requires you to rewire your fixture to take out the ballast and wire the power directly to the bulb connections rather than going through the ballast.
So you can replace the ballast and keep your existing bulbs (assuming they still work and haven't been damaged by the faulty ballast), or you can replace your bulbs and eliminate the ballast.
I had exactly the same situation in my house; I bought a ballast that looked like it was compatible, but apparently it wasn't because it burned up. Oops. I ended up just buying a whole new fixture because it was cheaper than replacing my bulbs, but your mileage may vary.