My iMac has a fan noise after it went off by itself during the havy winds last night.

It may be a certain mode that the iMac is running in. Here's a link telling you one way of solving the problem:

iMac Fans run at full speed after computer turns on

It may have shut down due to overheating. Here is a link with some solutions:

http://www.macworld.co.uk/how-to/mac/how-fix-overheating-imac-imac-overheating-tips-advice-3462816/

There is most likely a problem with the fan. Try relocating the TV to a flowing location

Check for blockage under the screen(by your ram slots)
the fan runs to cool the ram and other things! if you have too little ram the comp over works, so get more ram??

Your machine has a DVD-rom drive, but not a DVD-burner. There is a difference.

Basically, you can read and play the DVD's, but the drive is not capable of burning them.

if it is the drive itself then you will notice other things. Noise on start or a very slow start, hesitation on opening filesespecially large ones. If the drive is the problem then what you need to do NOW is backup any thing of importance to you. Things like documents, contacts, bookmarks and so on. Hopefully they will not have been corrupted by the drive but the longer you wait the greater the chance they will be or you will loose the ability to copy them off safely. You can then replace the drive and not have lost anything impotant. The other thing that will cause this is bad power. Either your power supply going out or your outlet fluctating.

Try calling Apple, tell them your Mac OS version and iMac's serial mumber, and ask them for a replacement install disc. They can ship them out to you for a small fee.

Go to the apple web site there are many write ups for screen and motherboard resets of the PMU. If not you mave have to send it in for service or find a local apple store to see if they can help.

Safe mode just requires holding shift down during start up and if it starts up at all this should be possible. Once in safe mode, you should be able to use Disk Utility to Verify disk and Fix Permissions. To Repair disk or with/without safe mode you need to startup with your install disk and on the first screen or after selecting language, use options to select Disk Utility. You really should tell us the MacOS version--10.3.9 10.4.11 10.5.8 or 10.6 are current and tell us your install disk version, too. With safe mode you can use terminal to run fsck to fix the disk, read the man page. Alternatives include starting up in Target Disk Mode (command+t at startup) and using your computer as an external disk for another Mac by Firewire or possibly USB, fixing it using the others software. These methods in descending ease.
A now permanently dark screen would indicate a bigger problem and a trip to an Apple store for an evaluation. Tell us your iMac model--could affect whether you can easily savage your disk data in this case. -Ken

you have to remember that electronics can have interference from wireless signals and etc. try moving your computer to different places in your house

Sounds like a power supply issue. You will need to take this to an apple dealer and ask them about it. This one is not an easy fix as it is a hardware fault.