Subwoofers pop then immediately produce no sound

Sounds like the two subs wired together might be too much of a load on the amp and it is shutting off. Try wiring the two subs in series. That will reduce the load on the amp but will conversely put out less power. Less is better than none though. In any case check your amp to see what the lowest ohm rating it can see, that ohm rating is where you want your subs and if faced with a choice of either going under (lower numerically) or over (higher numerically) GO OVER!-it is much safer.
Here's an article I wrote that can help explain how to wire the subs to the amp.

OHM LOADS, SUB WIRING, OHM RELATED POWER OUTPUT

SERIES SUBWOOFER WIRING
Wire the positive pole from one voice coil (using wire that is as thick or thicker than your wire from amp to sub) to the negative pole of the other voice coil (on the same sub). This will leave you with a positive pole from one voice coil and a negative pole from the other giving you the two leads that will be hooked up to the amplifier or other subs. When wiring in series, the ohms will go up numerically, and the load on the amp will go down. Almost all amplifiers power output will follow this rule, except some amps such as JL Audio's “Ohm matching” D Class amps.

PARALLEL SUBWOOFER WIRING
Wire the positive pole from one voice coil (using wire that is as thick or thicker than your wire from amp to sub) to the positive pole of the other voice coil (on the same sub). Then wire the negative to the negative in the same way. You can then wire to the amp or other subs. When wiring in parallel the ohms will go down numerically, and the load on the amp will go up. Almost all amplifiers power output will follow this rule, except some amps such as JL Audio's “Ohm matching” D Class amps.

MULTIPLE SUBS USING SERIES AND PARALLEL WIRING
In order to match your amplifiers ohm rating you can use parallel and series wiring together, just keep things even for power distribution and to avoid phase issues.
Example: I have two “Type X 12” subs” that have dual 2ohm voice coils and have to match my “Amplifier X” ohm rating of 2ohms mono. In this case, I would wire each subwoofer in series (giving me a 4ohm load), and then wire the two subs in parallel to get my 2ohm mono load. When wiring multiple subs just, treat each sub as a voice coil and wire accordingly.

POWER OUTPUT AND OHM LOADS
For example if “Amplifier X” can make 100watts@8ohms, it would make 200watts@4ohms and 400watts@2ohms. However with every drop in ohms the amplifier is put under more pressure. It starts to create a lot of heat, distortion figures begin to climb, damping rates drop, and some amps even throw power spikes when clipping. SO BE SURE TO CHECK YOUR AMPS RATING AND DO NOT EXCEED IT!

-Dynami