Iomega insists that my drive may or may not be in warrantee. It's been a weird series of calls. The upshot is that they're going to send me a replacement power supply (basically, the cable/adapter that plugs in to the wall) and a USB cable. Frankly, I have my doubts that it will work, but they might replace the drive anyway. I don't have the receipt, but apparently the Serial Number was sufficient for them to realize that it's less than a year old. I may be able to dig out the receipt or get a new proof of purchase from MicroCenter.
In the meantime, I don't want to be without backup. I'm probably going to get another terabyte drive. No, not another Iomega. I've found several (including a LaCie 2TB for a decent price but might just bite the bullet and get a high-end, recommended-by-the-data-recovery-place G-Technology drive as back up, and deal with iTunes later (probably after Marscon, alas).