The HD of my iMac stopped working so it wouldn't initialize after the gray screen. The assistance told me I had to buy a new HD for it and so I did, how can I transfer all the things that I had from my old HD (I've always used Time Machine) to the new HD? Will it have all the applications, data and software the same way it was before my HD crash?
First of all, after getting your computer again, turn it on and check if OS X is installed. If it's installed, follow the steps on the screen, because OS X should ask you to restore a backup.
If it's not installed, you have to install Snow Leopard with the DVDs which came with your computer. Then, after installing Snow Leopard, open > Software Update, and download 10.6.8. After that, upgrade to Mountain Lion, and finally, restore the backup with Migration Assistant. As you can see, the process is much more long, because the Late 2009 iMac hasn't got Internet Recovery and Time Machine backups aren't bootable, so restore is difficult