LED on same Pin as Toggle Switch, not illuminating
LEDs have a (fairly) fixed voltage drop across them.  The red LED is about 2V.

You can use that to work out the voltage at the input.  You basically have a voltage divider, with your 200Ω resistor as R1, and your 1kΩ resistor as R2.  The voltage drop of the diode is subtracted from Vin.

So:

Vout = (Vin - Vled) * (R2 / (R1 + R2))

     = (5 - 2) * (1000 / (200 + 1000))

     = 3 * (1000 / 1200) 

     = 3 * 0.833

     = 2.5V


The ATMega328P datasheet states that a HIGH input voltage must be over 0.6*Vcc, and a LOW input voltage must be below 0.3*Vcc.  That means to register a HIGH you need more than 3V.  To register a LOW you need less than 1.5V.

You're between those two voltages - in the "dead zone".

The simplest way to achieve what you want is to use a douple-pole switch and keep the LED completely separate from the Arduino.