Camera only half operates: preview mode OK, picture-taking mode not working

I have a Fujifilm FinePix E550. It's between 1 and 2 years old.
I went to use it the other day, and had it set to take pictures. (The little selector was slide in the up posistion for this). I powered it on, and took a picture. The batteries were low, so it died right after I pushed the shutter button. The lens is stuck out at this point.
I replaced the batteries with one set of brand new ones.
Now, when I hit the power button, the light next to the view finder flashed quickly, and you can hear the normal noise from it trying to turn on. Nothing shows up on the screen or anything though.
At first I thought it was a bad set of batteries, so I tried a 2nd set - same results.
I flip it to preview mode. Everything in that mode seems to work fine - but it powers off automatically after roughly 30 seconds. I don't remember if this is normal, like a power-saving mode or not. The lens never closes though, and I know it should when in preview mode, after an amount of time.
I tried going back to the picture mode, and it still is doing the exact same thing.
It's out of warranty, and taking it to a repair shop is really not an option here. I'd rather just buy a newer dSLR. I just need to know if there's any home-brew solutions I can try to get my camera fully functional again.
Thank you much!