You’ll get the same behavior of solid red and solid green LEDs if you power up the Pi with no SD card in the card slot at all. So I’m leaning toward an SD card problem.
If you have a Model B then it has a fairly limited amount of power for USB. If you have any USB devices plugged in that aren’t essential for booting, try removing them.
If you have a model B+ with the micro SD card then there is a real positive click, like a ballpoint pen, when you click the card in there so please make sure it clicks in there and seats well. On some B+ units it’s possible to pull the card out without pushing in to click it out so make sure it didn’t accidentally get pulled part-way out by clicking it out and back in.
The .img file should be exactly 3,276,800,000 bytes long. If you have a tool to calculate the SHA1 checksum of the file then it should turn out to be 22ba87ad82e83aa44865fd376655694f276a8659. If there is any deviation in the file size or checksum then your download is corrupted and yeah, about for sure it won’t work.
If you use a Mac to copy the img file to the SD card and you use the “dd” terminal command rather than the tool then there are a couple of files you have to delete on the card and then issue an unmount disk command.
If you have another SD card then try that. You might also try formatting the card with the formatter from the SD card association. It can do low level stuff to the card to fix the wear leveling tables that are maintained by the ARM processor on the SD card itself, behind the back of the filesystem. If those get corrupted then the card won’t work right and this can happen fairly easily like if a machine loses power while it’s writing or you pull the card out while it’s being written to.
I think the rate of Raspberry Pi computers turning up dead on arrival is low. Like out of a couple hundred I don’t think we’ve had any that didn’t work. I would put my money on that there’s some kind of SD card problem, but if you go through all the aforementioned stuff and have the same problem with a second SD card then suspicion will probably move to the Pi.
Please let us know what you find out. We are happy to try to help.