Hate to hear that it was the HU for sure, but at least now you can get back to jammin'!
You may have to change how the speakers are wired. If you replaced the front speakers or the factory ones are 4 ohms, and the new 4x6's are 4 ohms, and the wiring is wired in parallel you're presenting a 2 ohm final load to the HU amplifier and they're not rated for that. It could be the cause for the failure on your stereo. They can get by with that from the factory because the tweeters use a capacitor as a -6dB crossover that limits their playing range to only high frequencies to protect the tweeter. It also helps to protect the amp in the factory HU since it doesn't see the tweeter as a load on anything but those frequencies the capacitor allows to play. Those are typically in a range not played well by the woofer and naturally slightly filtered, like the capacitor does for the low frequencies (it's measurable but not extremely audible in the case of the woofer) also -6dB, by the inductance of the woofers voice coil. So with the capacitor blocking lows from the tweeter, and the inductance of the woofer voice coil limiting the highs the amplifier is, in a sense, only seeing one speaker as far as it's load is concerned. That and it takes VERY little power to play high frequencies by comparison to that of low frequencies at the same output level.
I hope that all makes at least a little bit of sense. If the factory wiring is indeed connected in parallel (and I'm fairly sure it is) then you could very well be overloading the internal amp in the HU with the 2 ohm final load. If you put good aftermarket speakers in the front doors a good solution to your problem would be to pick up a small two channel amp to drive just the front door speakers.