LCD screen black when photo being taken

This is not a problem: the LCD monitor cannot be used as viewfinder for shooting as with digital compact camera's or non-professional DSLR's.
This info can be found in the manual on p. 36.

Unfortunately the 5D (original) doesn't have live-view - which allows you to see the picture before you take it. It doesn't have video either but I guess you already knew that.

Sounds like the shutter control is not active. If closed, the shutter will not allow light to enter and thus you have a black receptor. Take to a camera shop for testing.

Sounds like you lost the connection to the sensor.

This sounds like it might be a defective CCD imager. If so, Canon should fix this for you for free, including free shipping both ways. This is regardless of your camera's warranty status. Please check this link for more info.
Applicable cameras include:
A40, A60, A70, A75, A80, A85, A95, A300, A310, S1 IS, S60, S200, S230, S330, S400, S410, S500, SD100, SD110, IXUS V2/V3/300/400/430/500/II/IIs, IXY Digital 200a/300a/320/400/450/500/30/30a

Hi,
Its known issue of ccd imager in DSC-T1 camera and Sony will repair it free of cost.
Click Sony CCD Imager Support for details.

Try cycling through the Display button until you're able to view photo to be taken.

This is normal for this camera. Think about it. The CMOS chip can't see through the mirror. After the shot is taken the electronic shutter exposes the CMOS chip and makes an image just like exposing film on a film type camera. Once you get used to it you may like it better. In outdoor or bright light situations it's difficult to view the LCD screen to frame the shot anyway.

The Display button manually turns the LCD display on or off to save batteries. If you accidentally had turned the LCD off, It should only take one press of the button to turn it back on and leave it that way. As such, it's not you but the camera. The A570 IS is relatively new. Your camera is likely still under warranty. If so, contact Canon for warranty repair (see the following link):

http://www.usa.canon.com/consumer/controller?act=PgComSmModDisplayAct&keycode=2113&fcategoryid=221&modelid=14905

there may have been some kind of damage to the lcd. sounds like you are going to have to send it in to have it fixed.