My rca lyra keeps turning on and off and when i hit the play button it shuts off and turns it self back on It turns on and starts to play but will shut off or if you try to go to the next song it shuts off. I don't know what to do with this.

Do you have the RCA LYRA PEARL, with the folding out usb plug? RCA has made bunch of different mp3 players and has reused the LYRA and the PEARL name. Mine has both names on it, and the firmware file below is for model numbers TC- or TH-1602 or 1604.

One time I replaced my battery and my unit would not go any further than the Pearl logo. So, I downloaded the firmware upgrade from http://voxrightnow.custhelp.com/app/answers/detail/a_id/2243/related/1, and followed all the troubleshooting instructions that popup when you start the program:

start the program,
remove the battery,
hold the play button while plugging into usb,
release the play button the the term "initalizing" replaces "searching",
check the box that says "format data" (you can try it first without this checked, it may work and will save your music),
click the start button to replace the firmware.

After I did this, my pearl started normally, and my computer recognized it again.

go to the thompson.com website and download the new software for your player.. 

check to see if its locked on the back ,lock button could be stuck or locked'

You need to switch the lock off on your LYRA. It is located on the back of the device between the pictures of a key and the word "off".

I used to own this mp3 and have had it for many years and it has froze up a few times but not like you describe it.

I can answer 2 and 3
2. I dont know what DSP stands for but it optimizes the sound for the genre you select. I personally liked the Rock DSP because it raises the bass.
3. Mode changes the playback mode dice is the shuffle and the circle thingy is if you have like 1 or 2 songs on it and don't want to keep pressing play after its done it automatically keeps playing until the battery dies. I personally don't use the circle mode because if you accidentally leave it on in that mode it drains the battery because it doesn't stop playing.

On the back of the player there is a button to the right. Above the button it says Off and below it there is a picture of a key. Switch the button upwards to turn the lock thing off.

change the battery, or send it back it may very well have a problem that Your warranty with RCA will probably cover.

Try updating the player's firmware, you can download it from the RCA Website (http://support.rcaaudiovideo.com/)
If your computer doesn't recognize the player, you'll have to turn it off and keep "PLAY" pressed for 10 seconds while connecting it to the USB port, then update the firmware.

you need a new hard drive they are really hard to find

I suggest you might need to clean up the cantacts of the buttery poles from corrosion or it could be they are broken or out of place