High voltage led detector
What you want is a simple comparator.  However, neither LEDs nor comparators run at 350 V.  You therefore need to divide down the input voltage to something in the range of what a comparator can handle.

Let's say you use a 9 V battery to power your detector.  You can make a 3.3 V reference from the 9 V battery with a single cheap chip and use that as the threshold voltage.

A simple resistor divider can scale 350 V down to 3.3 V.  The top resistor needs to ideally be 105.1 times the bottom.  If you make the top 10 M&Omega;, for example, then the bottom resistor must be 9.52 k&Omega;.

Many comparators are available with open collector outputs.  Arrange the output to go low when input voltage is above the threshold.  Connect the LED in series with a resistor between the 9 V battery and the comparator output.  Let's say you are using a red LED and want to run it at 20 mA.  That will drop about 1.8 V, leaving up to 7.2 V across the resistor.  By Ohm's law, the resistor should be (7.2 V)/(20 mA) = 360 &Omega;.  Just be safe, I'd use the next higher common value of 390 &Omega;.