View finder of canon powershot s2 is is black and can not take photo. Is there a way we can fix this problem.

Look into the lense while setting the shutter speed at a half second or so (slow enough for you to see the shutter open and close) and click the shutter release... you should see the shutter open and close. If you don't see this, then you may have a 'sticky shutter' resulting from lubricant seeping into the shutter/aperature mechanism and preventing the shutter from functioning as it should.(Common problem reported with the S2 and S3 cameras... and probably the S1 as well)

I have gotten my S3IS to take pictures by turning on the power, then opening the battery compartment door and reclosing it repeatedly until the shutter opens (from the power surge) and an image appears on the LCD.

After confirming the sticky shutter was indeed the problem, I pursued a more permanent fix.

this means there is a problem with your lens system. If Lens system seems ok then problem may be with the CCD/CMOS repairing which will be pretty costly and will need a expert hands to fix it.

A stuck shutter is another common failure mode for digital cameras, but especially so for the S2 IS. The symptoms of a stuck or "sticky" shutter are very similar to CCD image sensor failure. The camera may take black pictures (for shutter stuck closed), or the pictures may be very bright and overexposed, sometimes with lines, especially when taken outdoors (for shutter stuck open). To confirm a stuck shutter, put the camera in any mode other than "Auto", and turn the flash OFF (you don't want to blind yourself for the next step). Next look down the lens and take a picture. You should see a tiny flicker in the center of the lens as the shutter opens and closes. If no movement is seen, then you likely have a stuck shutter. If so, please see this link for further info and a simple fix that may help.

A stuck shutter is another common failure mode for digital cameras. The symptoms of a stuck or "sticky" shutter are very similar to CCD image sensor failure. The camera may take black pictures (for shutter stuck closed), or the pictures may be very bright and overexposed, especially when taken outdoors (for shutter stuck open).

To confirm a stuck shutter, put the camera in any mode other than "Auto", and turn the flash OFF (you don't want to blind yourself for the next step). Next look down the lens and take a picture. You should see a tiny flicker in the center of the lens as the shutter opens and closes. If no movement is seen, then you likely have a stuck shutter. If so, please see this link for further info and a simple fix that may help:

http://camerarepair.blogspot.com/2009/05/simple-fix-for-stuck-shutter.html

When the big LCD is black the view finder will turn on, right?
You need to replace a new hinge unit. Here is similar solution
How to fix an intermittent display LCD on Canon PowerShot S5IS

There appears to be an issue with the S2 IS after two years.  See the reviews on Canon's website: http://www.usa.canon.com/consumer/controller?act=ModelInfoAct&tabact=DownloadDetailTabAct&fcategoryid=322&modelid=11368#ModelDetailAct

If yours is two years old then you are probably out-of-luck.  It would probably cost more to repair than to simply replace.
You can at least save your photos by removing the memory card and reading the files using a memory card reader on a PC or MAC.

The symptoms are indicative of a CCD imager failure. But you can sometimes jog it back by trying the following:

http://www.fixya.com/support/t295396-canon_s2_black_screen

If the above works, recommend taking a photo at least once a week in a well-lit area to keep it running.

see http://www.fixya.com/support/t295396-canon_s2_black_screen for a fix

Sounds like you have a bad CCD. You can try contacting Canon to check out your options on how to get this repaired. Unfortunately the S2IS is not on their CCD recall list of cameras.

Is there a little black wheel or anything beside the optical viewfinder that turns? If there is, turn it until the image comes into focus.