You probably are not using the correct exposure.
In manual, it's entirely up to you to choose the exposure (unless auto-ISO is in use, and it can only help until ISO 100 or so). If the camera cannot find ISO that produces the correct exposure, or if the ISO is fixed, the image will be overexposed and thus white.
In shutter priority mode, it's entirely up to you to ensure the camera can choose the aperture (and perhaps ISO) to properly expose the image. The aperture can close only so much, until f/22 or so depending on the lens. Also, the ISO doesn't go below ISO 100. Thus, if you're already at ISO 100 and f/22, the camera cannot make the exposure darker. Therefore, the image will be overexposed and thus white.
Also, if the exposure time is long, the image will be blurry too. This, along with the white image, suggests you are using too long exposure time.
What you didn't say is:
- What is the exposure time you chose in the manual and shutter priority modes?
- What are you trying to achieve with the long exposure time? A white and blurry image says you're using too long exposure time.
If a blurry effect is what you're looking for, and you are shooting in ample light, there are neutral density (ND) filters that help you properly expose the image with long exposure times.