What did I fry?

A hard one since there would've been a spark anyway. Also, it's hard to tell, from your description, how you made the connections.

Probably

Just a guess that a tow to your friendly neighborhood Lexus dealership is probably in order. If out of warranty, you'll need to have your checkbook handy.

Did you check the fuses?

I would check the fuses before calling that tow truck.

From the description of "car starts and runs, but instruments and accessories out" I'll bet you popped one or more fuses. And yes, a short burst of backwards jumper cable power can easily do that, and screw up other stuff, too. Get a test light and start checking.

And there is an interlock solenoid on the shifter so you have to press the brakes before shifting out of park. No brakelight fuse = no power to the interlock solenoid = no shifting out of park...

Read the owners manual on the transmission shifter, there's usually a way to bypass that brake-pedal lockout so you can drive the car to a mechanic. You may have to take a little trim cover off the shift handle or center console, and stick a pencil in the hole to push in the solenoid plunger by hand.

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You have blown the main fusible link in the fuse box under the hood. I would guess this is probably a 100A one. Pop the fuse box lid off under the hood, close to the battery. There should be a few large fuses there with clear plastic see-thru tops that allow you to inspect the fuse element. One of those has blown. This will disable all of your accessories, including the brake lights. In order to shift out of park, the safety interlock is looking for voltage on the brake line wire, since there is none, the interlock will not release the shifter from the P position.

The cables are bolted to these big fusible links from underneath, not just plugged in. Disconnect your battery and push or pull the blown fusible link until you can access the fasteners. Replace it (you can get these at Pep Boys for a few dollars) with a new one, snap it back into the fuse box and reconnect your battery. Most of your accessories and brake lights should now be working again.

More than likely you have also blown a couple of other fuses so check all of your equipment and for anything that is found not to be working, investigate the fuses. My daughter crossed the jumpers on her Toyota and caused all the same symptoms you mention. In addition to the main fusible link, the EFI and radio fuses were blown as well as one of the dash lights. Good luck.

Too damn right, check all the obvious things first, THEN take it to someone if you still have no idea.

First of all, thank you to everyone who replied. With all of the beaters I had in high school and college I did a lot of jump starting. I can't believe I've never made a mistake like this before. Anyways, I'll look into your suggestions first, hopefully tonight.

Looks as if you are correct, I popped the lid and staring me in the face was a blown 100A fuse. Problem is that when I pulled the fuse only the housing came off, the 'legs' remained I assume welded in there. Uggh

Yup, that's what I thought. That big fuse is bolted to it's cables. You can't just unplug it. It should be possible to push the fuse out of the bottom of the box (you may have to loosen up the bolts holding the box to gain a little access) with its cables still attached so that you can get at them with a small wrench. CAUTION - be sure to disconnect the battery before messing with this!

I was able to disconnect the box from the sidewall, I just can't get any access!

You're going to have to get the blown fuse, wires attached still, clear of the box. In my case it pushes out through the bottom but I recall using a screwdriver or some such to release the little retention tabs. Without seeing your exact situation, (I have an IS300, which I think is the same.....), I can't say for sure.

Looks like someone already mauled the little retention tabs, thanks for the help, I may need to give up on being too stubborn to pay the dealer for something so small.