That's all horrible advice. The battery is just as user replaceable as a CD drive or the RAM on the original mini. While it's not meant to be done, it's possible!
Taking the mac to the Apple store and crying to a "genius" will only flag your mac as no longer under warranty, and unless you want to pay $$$$$$ to have Apple fix it - no 3rd party solutions allowed this time - Apple will consider your machine's entire warranty null and void. In their eyes, if iMovie stops opening, it's due to the damage you inadvertently caused when you disassembled your mac, and if you want warranty service again, you need to pay to have Apple fix both the battery AND iMovie (because you broke iMovie when the mac wasn't under warranty).
So now for some real help
Open up your mac, again. What happened is that one of the wires that connects your battery to the motherboard isn't connected. Although the battery is connected to provide power, the wire that tells that computer that the battery is physically present isn't connected. I had the same problem when I pulled my mac apart to replace the bottom case. Pull the computer apart, check all of the wiring that goes to the battery, and try again.
If you're not comfortable doing that, you could always take it to a computer repair shop - not an apple store - and have them do it. It's cheeper than an Apple store, and they should be able to get the job done.