Could be any number of things. Sounds like the power button might be stuck and the camera is going into the start up and shut down cycle over and over. Or...possibly the battery might have been damaged and is not suppling enough amperage to keep the camera running.
It would be best to take it to your nearest Best Buy and have the Geek Squad take a look. They will advice you what can be done.

A viewfinder is not necessarily a “Have to Have” feature. It is very helpful in situations where the LCD Screen is difficult to see. I find the looking through a viewfinder helps me compose a better shot by allowing me to concentrate on just the area of the photo without the distraction of everything going on around it.
There are Glare Reduction covers you can put on LCD Screens to help in bright sunlight and fold out shades that attach to the screens. Any of these can help, but still are not a perfect fix.
There are several Compacts that have viewfinders and many of the Advanced Digitals do. Of course all D-SLR cameras have viewfinders. I would lean toward the D-SLR ...better photos, more reliable, easier to use, longer battery life and more lens options. After all...how often are you going to get a chance to go to Australia?

All D-SLR cameras have a view finder and some models have live view. Very few manufacturers make compact cameras that have a view finder however Canon does have several models that do. Starting with the DS1100IS found here:
http://www.bestbuy.com/site/olspage.jsp?skuId=8742239&type=product&id=1202648739174
Other models include the SD890IS,SD770IS, SD990IS and the new SD780IS

If you are asking if there is a two camera bundle...none that I am aware of. If you are looking for a digital camera that takes both video and still photos, many of the compact digital cameras have a Video and Audio recording function (movie Mode). These are of limited quality but still surprisingly good, mostly of a quality with uploading as e-mail attachment in mind. Some models can record at 30fps (frames per second).
Almost all video camcorders have a photo function. The quality has improved to be as good if not better than some compacts.
If you want the quality of a D-SLR camera and still want great video look at the Nikon D90 found here:
http://www.bestbuy.com/site/olspage.jsp?skuId=8975184&type=product&id=1217633560861
It is the World’s first D-SLR with an HD movie mode. It can record cinematic-quality 24fps movie clips with sound at up to 720p HD (1280 x 720 pixels) in Motion JPEG format, enhanced by NIKKOR interchangeable lens quality and versatility