Is there a fix for an improper joystick input signal (and console...

The question would end in “(and console powering down)?”. There is a crippling problem with the DUALSHOCK 3. Even when I am not pressing anything, the controller seems to send a signal that the right-hand analog stick keeps being moved down. This does not stop and makes it impossible to play some games or select some settings. Is there a fix? (Note: Before I can get to this, I will need a fix for the PS3 shutting itself off as if someone pulled the plug out after 3 seconds on, turning red upon pressing the power button again after a few seconds. It does not work for about 1-5 seconds. Upon pressing the button again, the light turns green, then the pattern repeats after 3 seconds. Changing the angle can keep it on for about 20 more seconds on occasion, however.)