Grinding/Wheezing Noise on Attempted Start-up (Full electrical power, but no start)

I have enough of an update from my previous post that it might merit starting a separate thread. If you want the full background that can be found here:
http://community.cartalk.com/discussion/2295819/replaced-coil-pack-now-turning-the-key-does-nothing/p1

Here’s an abridged version: 1997 Ford Escort. Started idling rough, cylinder 3 was misfiring, I determined the most likely culprit to be the coil pack. Unfortunately I had to drive the car again, it stalled on highway and wouldn’t start again. Turning the key resulting in the same sound it makes now (with full electrical power, dash, cigarette lighter, interior lights, radio…) but wouldn’t start. Popped the hood open, and little streams of white smoke were coming out of all 4 spark plugs and their wires were loose. In my mind, that severely increased the odds that it had been the Coil Pack which had now blown out and in probably a surge of power took the spark plugs with it. Had car towed to my apartment and I ordered new plug wires & coil pack.

Fast forward through some winter weather & a trunk light left on and once the ice melted I replaced the coil pack and spark plug wires (was then going to pick up the plugs from local store) and found the battery 100% dead. Yesterday Walmart replaced battery for free & I got plugs. So now we have:
New plugs
New plug wires
New coil pack
New battery
<1.5yr old rebuilt alternator

And the car won’t start. Turning the key gives power to everything - lights, dash, etc - but results in just a sort of grinding noise, maybe a little more wheezing? My initial impression was that it’s a similar sound to cranking a generator, that sound of metal being moved rotated around other metal or something. I have an audio file of the sound on my phone, I’ll use that to reply to this post with the clip. Current theories include: something wrong with starter (various possibilities, all of which likely mean i should probably just replace it), a bad solenoid, a broken timing belt.

The good news is my roommate’s car will be out of the shop after work tomorrow, so this stopped being the stupidly urgent matter of balancing my repair costs with rental car costs in a desperate attempt to get 1 car running before running out of money. Still, I’m down to my last $110 on this and the sooner I’ve got my car up & running the better. With only that little money left, just getting it towed to the place I trust most in my city for repairs would run me dry, so I’m trying to at least self-diagnose & get as much of the repairs done myself as I possibly can.

Thanks everybody. The generosity of this community continues to astound me and I absolutely could not have handled this situation at all without you guys.

Audio.

My best guess is there is no compression in the engine. It sounds as though the starter is spinning a free wheeling engine. Very possibly a bad timing belt.

After listening to the audio myself I have to agree with @Red Knox, it appears the engine has no compression due to the valves not working because of a broken timing belt.