replacing blown boston acoustics speaker

Audio stereo speaker systems are routinely sold and listened to in pairs...left and right channels.  Buy what you need to replace the pair when one speaker system fails.  The old good one is still good, it just doesn't have a mate.

They could very well have been packaged individually for their best protection during shipment, although intent was that they were sold in pairs.

Your original front stage speaker sets must certainly have passive crossovers, located between the amplifier and each speaker (woofer and tweeter) on each side.  The crossovers use the available frequency band from the amplifier's high pass crossover to direct portions of the band to each of the system's drivers.  It likely also controls sound characteristics by "padding" (reducing input) to the tweeter, or other sound improvements, to complement the total sound from the system.  These crossover components are just hidden from view.

From that, you know there are two types of crossovers at work here.  The amplifier sends higher freqs to the frontstage speakers, which are, themselves, separated into components.  So the amplifier's job is to keep lower sub bass freqs from getting to the front speakers.  It sends those to the sub woofer, and that type of crossover is built within the amp and is called "active".  The front speaker components have to have their own crossover to separate the music signal and make whatever adjustments are necessary, and these crossovers are known as "passive".

Given all that, you are looking to make a swap.  After reading all materials you get with your new system, connect them in place of the original speaker systems directly to the amplifier.  Use the crossovers that are provided.  When you disconnect the original speakers, you are also disconnecting the original passive crossovers.  The flow is:  amplifier > passive crossover > speaker

You may want to run new wiring.  That's what I would do.

What you're looking at on that amp is the standard 12db / octave active crossover.  You can select either HP or LP on channels 1/2, and same choices on channels 3/4.  Typically, two channels will run front soundstage and the other two channels will power either a sub (by bridging the channels), or a second pair of speakers in the rear.  Either way, the crossover adjustment of "30 to 400 Hz" is typical of the selection range for adjusting between high pass and low pass.  It us usually set at 80 Hz or 100 Hz, but there are sometimes reasons to vary the mark a little lower or higher. 

FYI the crossover range from midrange woofer to tweeter is around 3,000 Hz, sometimes up to 5 kHz.  Simple systems such as coaxials use nothing but a small capacitor built directly onto the speaker to filter the range of music that reaches the tweeter.  The mid woofer has no help or limitations on this type.  These types are certainly not nearly as good as separate components with passive crossovers, which contain capacitors, inductors (coils) and usually also resistors.

If there is no passive crossover, then you might be talking about coaxials?  I didn't look up the speaker that is installed in your car, but if the pair have separate woofers and tweeters, follow the wiring from those components and the wires should lead directly to the passive crossover.  The crossover is also wired to the amplifier.  If the passives were left out, I don't know how the tweeters survived or how horrible the system sounded.

Do yourself a favor and read the help sections found on the left side of this page, starting with https://www.the12volt.com/caraudio/caraudio.asp

Repair it and give it a try.  I'd use adhesive caulk to glue it back in.  When it sets up, reinstall it and try it out.  If it plays okay, you may want to take this opportunity to do a little work on those two front doors, by damping the sheet metal with Dynamat or similar, and otherwise taping up and sealing any air gaps you can find.  You would experience a better bass response.