you need to bypass the factory amp
That's not entirely true.. I just hooked up a new stereo to my 97, and was having this same issue w/ no sound.. And I planned on bypassing the amp, based on info I read here.. But in my thread I made, you'll see that someone said you CAN wire up the amp and it would sound good - and after just having done that, I can vouch for it.. As long as your volume/eq levels are in check, it sounds totally fine, no distortion whatsoever, and the bass has more of a punch to it.. There's a fine line however, where it COULD sound crappy, but as long as you know where it is, and you have the proper volume/eq levels, it has the capability of sounding good..
Now to the original poster, I think I know what your problem is - you have the wrong harness.. For that year Explorer, there were 2 different harnesses.. They have the same power plug, but different speaker plugs.. And judging by your description of how 1 of them fits, and 1 doesn't, that's exactly what it sounds like.. Your options are getting the right harness, or cutting the speaker plug off and splicing the wires yourself.. I would personally get the right 1, as the 2nd option is gonna be somewhat of a pain in the a%$, since you have to literally do all the work right inside the dash, cuz you only have about 1 ft. of slack on that plug.. If you're good with that stuff, then go right ahead and do that, but keep in mind if you ever have to swap the stock deck back in, you're gonna have another project on your hands..
Now as far as the stock amp, if you wanna continue using that, I think you NEED the right harness, cuz it has an amp ground wire on the speaker plug.. On the 1 you have, I really doubt it's on there.. But if you get the right harness, you just wire that amp ground right into the main stereo ground, and you wire the 12v amp wire (which you also wouldn't have I don't think) into the power antenna wire to power it up.. Now if you have the system with the subwoofer as well, I'm not sure how that would sound using the stereo and stock amp, since I don't have a sub on mine..
The other option of bypassing the amp is ANOTHER pain in the a%$, since you need to buy another "bypass jumper cable" and remove the rear quarter panel.. I actually removed the panel in mine earlier today, and while it wasn't that hard to do, it definitely wasn't an easy beginner-type thing.. It actually is possible to do w/o the jumper cable, but you'd have to cut 2 plugs and splice the 8 wires together.. I wouldn't recommend that at all tho, since the wire colors do not match up, and you'd have to either KNOW which wires match up properly, or figure it out for yourself with a voltage meter or something.. And with that option, you'd have to do all the work right there in the cargo area.. If you try and do that, and manage to get the quarter panel completely off, then you're gonna see why I would not recommend that option.. And if you can't get the panel completely out (I only had mine halfway off), then you'd be hard-pressed to even disconnect the plugs, nevermind cutting them off and splicing the wires.. That's how tight it is back there..
Your last option for bypassing the amp is to run brand new speaker wire directly from the deck to your speakers (removing door panels and running it thru the door jambs), and that would actually eliminate the problem you're having with the harness, since you wouldn't be using that plug at all.. But out of all the options, that would the most difficult and time consuming..
So just having done this today, those are basically your options.. Good luck