I recently constructed a NOR gate using the following schematic but when one of the transistors is set to HIGH an led I connected to the output of the gate glows brighter, but the other one works just fine. What's causing this?
It looks like you have a NOR gate now, albeit non-standard RTL input levels. TTL is two diode drops and HCMOS is Vcc/2 threshold. The saturated gain of a transistor is only 10 to 20. So choose R values for a gain of 10 for reliable current switching.
CMOS NOR Gate
This is a simplified CMOS NOR gate with fancy triangular inputs running at 100 & 110 Hz to give a 10 Hz beat frequency on the output. Purpose is to show the linear input threshold. This uses n and p Mosfets to give low impedance for both output states, although the high side usually has a resistor to current limit it.