On my TI 83 Plus I can only get the first option under the 'apps' key to come up. The other four options do not come up. I can't fix this situation.

4 AAA batteries and one CR1616 or CR1620 button batter for backup

Source: http://en.wikipedia.org/wiki/TI-83_series

Please Install Calculator Software Now error
This message means that the operating system has been corrupted. These steps will allow you to update the OS.

Unit to Unit
• Connect two TI-83 Plus units by means of the data cable (short black cable that was prepackaged with the TI-83 Plus)
• Make sure that at least one of the TI-83 Pluses contains the current Operating System
• Select [2nd] Link
• Select "Send OS" option from the Link menu
• Make sure that the other unit still reads "Waiting Please Install"
• The OS should be downloading.

From the Computer
• Make sure you have the latest version of the TI Connect™ Software
• Download the latest version of OS for the TI-83 Plus to the desktop of the PC.
• Connect the appropriate TI-GRAPH LINK™ cable between the PC and TI-83 Plus.
• Since the TI-83 Plus is currently off, the TI-83 Plus will automatically turn on when the TI-GRAPH LINK Cable is inserted.
• On your computer, choose Start, Programs, TI Tools, TI Connect, TI OS Downloader.

There are a lot more than five apps available for the TI-83Plus. You can download them from
http://education.ti.com/educationportal/sites/US/productDetail/us_ti83p.html?bid=7

If you have MirageOS installed under the APPS button on your TI-83 plus, it may be blocking your memory menu. Enter MirageOS and press the ALPHA key. It may ask for a password which will have been set by the user. If so, you will need to enter it in. Go down to the option: Tasker and Key Hooks. There is an option that says: "Block the memory menu from access". Disable this, and you should be able to access the memory menu.

One way is to use the Polynomial Root Finder and Simultaneous Equation Solver app.

Press the APPS key, then select PlySmlt2 and press ENTER. Press ENTER to get past the opening screen, then select "POLY ROOT FINDER" and press ENTER. Select the order of the polynomial and other settings as desired. Press F5 (the GRAPH key) to go to the next screen. Enter the polynomial coefficients, then press F5 to solve. The next screen will show you the roots (unless you selected real roots and the polynomial doesn't have any real roots).

If you don't have the app installed, you can download it from
http://education.ti.com/educationportal/sites/US/productDetail/us_poly_83_84.html

Enter the number whose factorial you want to calculate.
Press the [MATH] key under the [ALPHA]key.
Press the Right arrow 3 times to highlight the [PROB] menu.
Select option [4:!]
Press [ENTER

Note : Due to memory limitation, the argument of the factorial function must at most be equal to 69

I am inserting a copy of an earlier post to a question similar to yours. Please read the post till the end.

A Try this before thinking of repairs.

1. Push the ON button.
   
2. Even if you see nothing, press the [2nd] key and release it.
3. Press and HOLD the UpArrow key until the screen darkens.
4. You may have to keep pressing UpArrow for a little while before you see anything.

B If that does not work

1. Remove one of the AAA batteries.
   
2. Press and hold the [CLEAR] key.
   
3. While holding [CLEAR], reinsert the AAA battery and then
   
4. turn the calculator on.
   
5. The calculator should display the message "RAM Cleared".
   
6. Release the [CLEAR] key and then press it one more time to remove the message "RAM Cleared".

C. Third option

1. Remove batteries including the backup battery for 5minutes.
   
2. After the 5 minute period, reinsert all of the batteries and
   
3. turn the calculator on.
   
4. Adjust the contrast if necessary.

D. Last option

The last option requires the reinstallation of the system. So to use it you must download the TIConnect 1.6 software from education.ti.com. You must have the TI USB SilverLink or the TI Black serial cable ready.You must be connected to the Internet.

1. Remove one of the AAA batteries.
   
2. Press and hold the [DEL] key.
   
3. While holding [DEL], reinsert the AAA battery and then
   
4. turn the calculator on.
   
5. The calculator should display "Waiting...Please install calculator software now".
6. Connect the TI Connectivity cable between the computer and the calculator.
7. Click on Start >> Programs >> TI Tools >> TI Connect >> TI OS Downloader.
8. Follow the on-screen directions to reinstall the calculator's OS.

If the message "Error! Press any key to turn unit off. Then turn unit back on." appears on the graphing calculator, quickly, remove one battery from the calculator and reinstall it while the transfer is taking place.

You have several ways to connect the calculator

• Serial Black cable that used to ship with the TI 83 Plus. It connects to a serial port on a computer and to the I/O port on the calculator. It requires the Graph Link software available on the TI web site (Downloads, Software and Apps, Connectivity)
• USB Silver Link cable. It connects a USB port on the computer to the the I/O port on the calculator. It requires the TI connectivity software, also available on the TI Web site.
  
• A USB mini A to mini B cable to connect two units.
• An I/O cable to connect two calculators through their I/O ports.

Do you mean four places behind the decimal point? Page 21 describes setting for fixed decimal point 0 thru 9 places to the right.
http://education.ti.com/downloads/guidebooks/graphing/83p/83m$book-eng.pdf

You must hit the "receive" button on the receiving calculator BEFORE you hit the "send" button on the sending calculator.

That is because the cable directions are wrong. The sending is B the receiving is A.