Automatic trans won't shift out of 2nd

This could well be just a sensor or shift solenoid.

I recommend a few diagnostic tests first to determine the seriousness of the problem.

First, check the oil. Level is important, but condition of the oil is more important. When you pull out the dipstick, look at the color. The oil should be fairly clear, and of a pink to reddish color. No flakes of metal should be present. Next, smell the oil. That't right! Smell it! It should smell just oily, and not have a burned or varnish-like smell to it.

Next, scan the system for codes. You can go to many parts stores for this. Many will do a free scan in the hopes of selling you parts. Take note of any transmission codes. NOTE that these codes do not nessarily light the "check engine" or "service engine soon" light.

Since the computer controls the transmission shifting, pressure, etc, it relies on sensors on the transmission to know when to shift, and what gear it is in, and which gear to command. Failure of either sensor puts the transmission into "limp-in" mode, which varies by manufacturer. Some have limited shifting available, while others default to a specific gear to allow you to get to a service facility.
Failure of a shift solenoid will not allow the computer to access the gears that the solenoid controls. I have to assume that it still starts out in first, then shifts to second, and then will not go to 3rd or 4th.

Give me more information, and I can tell you more specifically if the trans needs more than just electronic parts.

Good luck!