Why Can't my car go into gear?

First thing is check if there's a major transmission fluid leak. If there's an electronic problem it should default to second gear and stay there. Not moving at all is usually a sign of low fluid level or something seriously wrong inside the transmission.

The fluid is red. The dipstick will be to the left of center, (toward the driver's side), in front of the engine. The dipstick is somewhere between a foot to 18" long. If you're turning a cap and pulling it off with about a 4" dipstick, and the fluid is clear, that's the power steering fluid. That is on the far passenger side of the engine.

The proper conditions for checking the level are typically stamped on the dipstick, but for the problem you're describing, the level would have to be really low. Checking it improperly is not the issue. Normally they say to have the engine warmed up, run the shift lever through all the gears, (P, R, N, D, 2, 1, then back to park or neutral), then wipe off the dipstick and reinsert it to check the level. Running it through all the gears fills all the passages in the valves. That procedure is for fine tuning the level. If you check it cold, don't run it through the gears, etc, you're still going to see fluid on the stick. For what you're describing, if the level was the problem, it wouldn't be a fuzz low; it would be almost empty and you'd see a large spill on the ground. The typical cause of that is a ruptured rubber hose going to the transmission cooler in the radiator. Since you see fluid on the dipstick, something else is wrong.

One thing that is not real common but has happened before is a broken flex plate or the bolts that connect the flexplate to the torque converter have come loose and fallen out. The flex plate and torque converter are the coupling between the engine and transmission. If the flex plate breaks around the center where it bolts to the engine, usually there will be some noise associated with that like a banging noise, and once you stop the engine, it will not start again. That's because the starter turns the flex plate but the flex plate is no longer connected to the engine. If the bolts to the torque converter fall out, the starter WILL still crank and start the engine but since the flex plate is no longer bolted to the torque converter, it won't spin it and make the transmission operate. The clicking you're hearing could very well be the solenoids being turned on and off by the computer. Those are electrically-operated valves for the hydraulic fluid. The valves might be turning on but there's no pressurized fluid to flow through them.

A broken flex plate is a rather costly repair because it requires removing the transmission. I suspect that is not your problem though. Missing bolts to the torque converter is a relatively easy repair that could be done in less than an hour once the car is pushed onto a hoist. It would take longer if one or two of the four bolts is sheared off and has to be drilled out. When two or three bolts fall out, all the load has to be handled by the remaining one or two and that's why they give up and shear off.

P0734 †Gear 4 Incorrect ratio

Typically that means one of the clutch packs is slipping and the input speed, (engine speed) and the output speed, (road speed), do not match in fourth gear. Normally when any clutch pack has slippage that is detected by the computer, it goes into "limp mode" which is second gear. That lets you drive slowly to a repair shop without needing a tow truck.

An experienced transmission mechanic will make better sense out of that code but I suspect it was set because the transmission was in fourth gear when something broke. Based on the way it failed, I don't think it's related to a slipping clutch pack.

Definitely not. It means you get it professionally diagnosed first at a transmission specialty shop. With such an unusual problem two opinions are better but that might be impractical if towing it is involved.