I'm not 100% sure about this, but I don't think that the magnets are a part of the smart cover sleep/wake function. Pretty sure that this is handled by a sensor on the home flex, possibly in conjunction with a proximity sensor. The magnets simply keep the smart cover in place. Is it possible that you might've damaged the home flex in any way during the repair, or maybe that the glass isn't quite as adhered to the housing after replacing the LCD?
This is what the actual buttons look like on the inside (to the left in the image): http://applepartsstore.com/media/catalog...-2.jpg The yellow plastic covers with a tiny black "tit" in the middle of is the only thing you need to replace to resolve your issue. It's way easier than replacing the whole headphone jack part, and it shouldn't take you more than 5-10 minutes if you have experience in repairing phones. What's happened on your phone is that the tiny black "tit" in the middle of the yellow plastic has been worn out or, more probably, completely loosened from the yellow plastic. Underneath the yellow plastic there are two identical metal plates stacked on top of eachother, and it's very important to make sure that there's still two of them there when you replace the yellow plastic part. You simply order a headphone jack for an iPhone 4 or 4s, it doesn't matter which one, and carefully peel off the yellow plastic part from your old volume-up button and discard it, and then carefully peel off the...
Sounds like it might not have been the battery that was the culprit in the first place. Do you have a new charging port to try? Worst case scenario it might be an IC issue, more specifically the U2 IC might be fried.
What kind of repair have you done on the phone? Sounds like you might have messed up a component or two on the logic board. Take a good hard look around the antenna connector below the battery connector and see if anything looks scratched, damaged or missing.
Did you turn the phone off before disconnecting the battery? Did you disconnect anything else before disconnecting the battery? On some phones, disconnecting the LCD before disconnecting the battery burns a backlight filter or two, or even other components related to the LCD.
It probably can, but the question is if it's worth it. You'll probably need to replace the mid frame, the screen and the back cover, and that seems to total out at around $200-300. I'd give Samsung a call and see what they'd charge you for a replacement unit.
Are you sure that it's not turning on? It might just be that you damaged the LCD. Try plugging it in to a computer and see if the computer recognizes it or not. If it does; the device is on. If it doesn't; it is indeed not turning on.