My sons psp is not showing the start up menu. When turned on a wave goes across the screen and a loading circle appears in the right hand corner

Hi there.
Try increasing the PSP's "CPU Clock Game" by doing this;
1. In the main screen, press "SELECT" button and XMB or VSH Menu shows up 2. Scroll down to "CPU Clock Game" which is usually second from top 3. Press "Arrow Right" until the value on the right shows 333/166 (300/150 will also do).
I hope this solves your (and your son's) problem...

wait, so when you turn it on, the wave shows or nothing shows? and to turn it back off you have to hold it for like 30 seconds.

Take it back to the store you purchased it from and exchange it for another one.

your sons psp is bricked download this and follow what i say Pandora Deluxe 1.2 and this 4.01 official firmware
Open the Pandora Deluxe 1.2 and install.
Unrar the 4.01 official firmware and place the EBOOT.PBP in a folder on your desktop named 4.01.

Connect your PSP and enable USB. Start the Pandora Deluxe 1.2 program, while it is starting it will ask you if a certain drive letter is your PSP, make sure it is correct and click ok.

Click on the "Load 4.01 firmware" button and it will ask for the location of it. Find the 4.01 folder on your desktop, double click it and it will show EBOOT.PBP, select it and clickk OK. Then check the install box next to it. In the colum to the right select "Despertar Cementerio v7 (4.01m33-2)". Now just below that in the center is a drop down box with DCv7 next to it, drop the box down and select LEFT. In the box right below it check Format + Prepare Memory Stick, If you need to backup your memory stick select it. Make sure that the PSP Drive letter is correct and when you are ready to start press START.

When the operation is complete, disable the USB, disconnect the PSP and turn off. Remove the battery. Hold down the LEFT Trigger while inserting the PANDORA battery and continue to hold until the menu comes up.

Select NAND operations, then IDStorage tools. In that follow the prompts on the screen. Select your region, then turn on wifi switch and pres x to Get Real Mac and continue on till finished.

try updating the firmware to this

http://exophase.com/dax/

turn off your PSP ,then switch on again.. when the screen are in black condition "press R button" and change the CPU speed

Go to psp recovery menu and set the CPU speed in XMD to default, it should work

Are you running with custom firmware like M33 or HX?

If so, you can switch your psp off (not stand by), and hold R trigger when you switch it on, it should bring you to the recovery menu, where you can setup your XMB cpu speed and Game cpu speed, both set to default will be fine.

The last CFw Update is 3.71M33-3.

What is version on your PSP? (on PSP Menu, move across to the "Settings Menu". Scroll down, select to "System Settings" > "System Information" and you should see version of your PSP.)

Here's, how to install CFw Guides. Hope this be of some help/idea. Pls post back a detail should you need additional information. ^_^

Does the PSP have oe firmware... and did you try to reflash with another theme? If so try restarting with the right shoulder button pressed down to access the recovery menu and if you google 'semi-bricked PSP' that will show how to re-flash to firmware 1.5! Alternatively the screen my need replacing, which is a relatively easy job. As an ameteur I did it in 5 mins!