Okay, so what does its voltage measure unloaded and loaded, and does the loaded voltage change when you toggle the bias switch?
I hope that's not literally true. You can damage NiMH batteries by draining them too far. 0V is very very bad. You shouldn't go any farther than about 0.8 V per cell, or about 5.6 V for the entire battery in this particular case. (8.4V = 7 cells for a NiMH.)
Do you have a big power resistor on hand? If so, you can put it across the battery contacts, then measure voltage drop across it to infer that the trickle charger is working. V=IR, so if you use a 10 ohm resistor, you'd expect to see 0.2V across it if you set up the trickle charger for 20 mA, as would be appropriate for a 200 mAh battery.
You'll want to use at least a half watt resistor in this case. Power dissipation is 0.4W, so a 1W or bigger resistor would be better.
Or, you could put your ammeter across the battery terminals to measure the thing directly, though if something is very badly wrong, you risk blowing up the meter or its fuse. The resistor test is less risky.
It's a pretty crude test, so it's hard to say for certain, but that result doesn't jump out at me and scream "FAIL!". The actual values depend on details of your circuit build and, crucially, on how your meter works. Without a result down in the 100 ohms or less range, I think you've ruled out a dead short.
By the way, the 9.8k is your RLED, in all likelihood. (The result I was looking for is the 11.61k.) If so, and you used a 10k resistor, then either:
a) you didn't use a 1% resistor
b) your resistor is out of spec, or
c) your meter is el crap
Most blue LEDs are at least 3.7V, and some go as high as 5V.
You can test whether your battery voltage is too low by running from your wall power supply, which should be considerably higher voltage than your battery. If all the problems clear up on wall power, then you know you just don't have enough voltage to do what you're asking of the amp.
Few meters do a good job of testing Vf of LEDs. Many meters don't test with enough voltage to light the LED at all, and some that will light the LED don't give the right measurement. Diode testers on DMMs are typically intended to test regular diodes only, not LEDs.