The assumption before troubleshooting is that the lamp module or wall switch is in working order. This troubleshooting guide is for troubleshooting the SSR PC board. One of my mods did not work so I am documenting here what to check. A basic volt meter is all that is needed to check basic operation.
A basic check is to see that voltage is getting to the board on the lamp module or wall switch. If a negative probe is placed on pin 2 of the X-10 chip (18 pin IC), with the positive probe on pin 18 of the X-10 chip, the voltmeter should register -15V DC. Switch the meter to AC with the negative probe still on pin 2 of the X-10 chip, you should see line voltage (~115V AC) when you touch the neutral line. If there is no -15V DC, check the zener diode. If there is no line voltage, either what is perceived is the neutral wire is not or there is something really wrong with the power...
If the board in the lamp module or wall switch seems OK, I would move to the SSR circuit. Measure the DC voltage across the capacitor. When the X-10 module is first plugged in, the DC voltage across the cap should be nothing or really low. This is when the module is in the "OFF" state. Push the button on the wall switch or send an X-10 "ON" command to the module and the voltage across the cap should be greater than 5 volts DC. I usually see 7-10 voltages typically. If there is no voltage, either the X-10 chip is blown, the cap is wired wrong, or the wires from the cap to the module board is not connected correctly. The V+ signal on the SSR board should be connected to a logical ground (same as pin 2 of the X-10 chip) and the V- should connected to the collector of the transistor (where the 39 ohm resistor used to be).
Turning the module off by sending an "OFF" command to the module or pressing the button on the wall switch should bring the voltage down across the cap. The voltage should be zero or close to zero. If there is 15 volts, there is an open circuit between the positive terminal on the cap and pin 1 of the optoisolator or an open between the negative terminal on the cap and pin 2 of the optoisolator. The cap is staying at 15 volts because the LED in the optoisolator is not drawing any current. With the module unplugged, measure the resistance between the postive terminal on the cap and pin 1 of the optoisolator. If the 1K resistance does not show up, there is an open circuit somewhere between the cap, resistor and pin 1. This was my problem once. I had a bad solder joint at the resistor. The other option might be that the optoisolator is burned out.
The next place I would check is the output of the optoisolator. Switching to AC scale on the voltmeter, place a probe on the neutral wire. With the other probe, check the AC voltage on pin 6 of the optoisolator. There should be line voltage there. Now check the voltage on pin 4. When the module is off, there should be little or no voltage. When the module is switched on, pin 4 should show line voltage. If the line voltage does not switch on and off when the module is switched on and off, the optoisolator is probably blown.
If things have checked out up to this point, the alternistor may be blown. With a probe on neutral, there should be line voltage at the MT2 (center) pin of the alternistor. With the module on, there should be line voltage on the Gate pin and on the MT1 pin of the alternistor. If there is line voltage on the Gate and nothing on the MT1, the alternistor is probably blown.