I have a targus wireless mouse MODEL:AMW1603EU the reciver light does not come on and the mouse light doesnt go of nor does it work.

The battery cover is the part of the top of the mouse on the opposite end from the scroll wheel. Turn the mouse upside down with the scroll wheel away from you. On the end closer to you is a latch (called a "hinge" in the user manual) for the battery cover. Depress the latch and slide the battery cover off of the end.

The user manual is at
TARGUS AMW1603EU User Manual

Reinstall the drivers

you know it always happens on a wireless mouse so thats why im not recommending to use wireless intead the best is use an ordinary optical mouse.

The issue could be due to the corrupted drivers or with the hardware.
I recommend you to reinstall the mouse drivers from the below link:
http://www.targus.com/us/support_downloads.asp
Select your targus mouse model from Mice and Pointers option and reinstall the drivers of it.
Visit the below link for troubleshooting targus wireless mouse:
http://targus.custhelp.com/cgi-bin/targus.cfg/php/enduser/std_adp.php?p_faqid=645&p_created=1117141909&p_sid=-AiANoBj&p_accessibility=0&p_redirect=&p_lva=&p_sp=cF9zcmNoPSZwX3NvcnRfYnk9JnBfZ3JpZHNvcnQ9JnBfcm93X2NudD0zNzQsMzc0JnBfcHJvZHM9JnBfY2F0cz0mcF9wdj0mcF9jdj0mcF9zZWFyY2hfdHlwZT1hbnN3ZXJzLnNlYXJjaF9ubCZwX3BhZ2U9MQ**&p_li=&p_topview=1

Mine did the same thing, so I took it apart. The flip hinge in the receiver wore through the wire running between the plug & the little board inside. I'm shopping for a new mouse.

buy a new mouse

I think my mouse is not moving because one usb is missing. I
have trouble find one usb that can help move my mouse.

There's also a connect button on the USB connector. Plug the connector in and press the connect button underneath until the light flashes. Release the button and click the connect button on the mouse until the USB light is steady.

I had this happen to me after reprogramming my tv remote too close to my laptop and mouse. Try resetting the reciever and then the mouse by pushing the reset buttons on each one while they are plugged in ( reciever first, then the mouse ).

I assume this is a wireless mouse, Is there a similar button on the reciever? press this at the same time as pressing the one on your mouse