Cross connected jumper cables on 199 corolla. Car now turns but will not start

Are you asking how to hook up some jumper cables? If so, connect the two leads on the car you're jumping to the positive and negative terminals on the battery. Then connect the leads on the other end of the cables to the positive terminal (same cable as on the car to be jumped) on your battery and the other lead to a good "ground" (a manifold bolt, chassis bolt or - least desirable - the negative terminal of your battery). Be careful not to touch together or cross/switch the leads on either end of the cables once one end has been connected.
If that isn't what you're asking about, post back and we'll go from there.

Check fuses in fuse boxes, posible blown fuse. what kind of car?

cross jumper cables??? check main fuses..

battery is dead try to pair of jumper cables connected the same way as a single jumper cable this increases the cross sectional area of the wire causing more current flow

Might need to check the main circuits for a blown fuse or fuseable link.
There is a fuse wire between the alternator and battery.

TAKE OF BOTH CABLES AND GROUND THEM TOGETHER FOR 30 OR SO MINUTES, THIS WILL RESET THE CARS MEMORY, TEST VOLTAGE ON BATTERY WITH VOLT METER & IF IT IS BELOW 12.31V THEN CHARGE THE BATTERY , ONCE BATTERY CHARGED HOOK UP BATTERY LEADS (TO RIGHT TERMINALS) & ATTEMPT TO START CAR, IF ALL YOU GET IS A CLICK THEN LOCATE THE STARTER MOTOR & GIVE IT A FIRM WHACK WITH A HAMMER (SERIOUSLY) THIS WILL FREE UP THE STARTER & WILL ALLOW THE CAR TO CRANK

Check for the code on the computer to see if there is a code set for a particular system.

A 2005 Toyota Corolla would use an obd-II scanner to retrieve codes.

Something may have burnt out in addition to the fuse when the wires were crossed when jump starting.

Bad solenoid

Look for a lose connection at the crank shaft sensor. This is a signal needed for obtaining tachometer as well as turning on the fuel pump.

whats it doing