You ran the volume cranked to get the loudness that you weren't getting because you weren't feeding them enough power to get them loud at a lower volume level. This put you closer to clipping the HU signal. Compounded by the fact that if you crank the bass even a little without the proper crossovers in place to insure they're not getting a full signal, they get more bass than they can safely handle for extended periods and the extra bass boost decreased the speakers' power handling and put you closer to being over your head unit's maximum undistorted output. Every time the bass went to max for a few seconds it cut some more time from their lifespan. Loudness put you over the top, sent them way too much of a signal, distorted your head unit's output, and fried them. Any Alpine/Pioneer/Whatever kind of amp putting out 40-60 watts would do the trick. Some people aren't big fans of Best Buy here but you don't need big power for them so a cheap brand name amp from somewhere like that will do. 2 or 4 channel depending on how many speakers you want to power. Id recommend two and just worry about amping the fronts.
Set the high pass at 70 or higher, zero out the bass and treble, and figure out what you have to do to get the sound you want without your system straining. If you needed loudness and high volume and bass +2 it means you had to overwork your stuff to get the sound you want. Comps with no amp seems cheaper and simpler and alot of people try it first but it usually isn't cause you just spend more $$$ to make it better later.
To paraphrase the saying gun owners always used, under powering and overpowering doesn't blow speakers. People do. You could take any set of speakers and run it at either 1/5th or 5 times the power they need all day every day with the volume barely nudged past two and they'll never melt down. It's what the user does with the HU controls and amp controls when our setup isn't giving us the sound we want that blows speakers. For a set like yours, most head units are rated similar to yours which is 16 watts rms, which means realistically at normal levels you're probably sending them anywhere from 5-10 watts. An amplifier rated for 40 or 50 watts would ensure the speakers are are receiving enough power on a continuous basis to get as loud as they should. This is why it is generally recommended to match or exceed the speaker's rms rating slightly so you get the volume and output you're looking for at moderate levels without being tempted to do something that will eventually kill them.
Eclpipse SC 8362 front 2 ways
Infinity Reference Rear Coaxials
Eclipse EA4200 mid/high
Alpine MRP-M500 sub amp
Pionier Premeer shallowmount 10
Alpine CDA 9883