Can't get to BIOS

Did you change something in the BIOS before this problem?

Windows 8 & 10 have changed the way we can get into the BIOS. In the following link you'll find 3 different ways
http://www.howtogeek.com/126016/three-ways-to-access-the-windows-8-boot-options-menu/

This quite possibly is the issue.
The white circling dots animation is windows booting up.
So I am wondering just how many seconds go by before you are seeing this.
Some computers if they are set to the quickest boot up priority can be really fast here like 2 seconds.
If this is the case pressing and holding Delete might be the trick.
But in the off chance that your keyboard is a USB and not PS2 style it just might be plugged into a USB3 port or some other extra USB port that requires the OS to be loaded in order to function. In that case your keyboard may not be registering until the OS boots at which point you'll never get in. LOL
Most time at post the keyboard Caps Lock, Num Lock, and Scroll Lock lights (if so accessorized) will flash on at some point.
Your Num Lock light may or may not stay lit at this point depending on if it is set to be in engaged at startup in Bios or not. But if you have any lights that can light up on your keyboard you should see something happen with these before the dreaded white dots begin spinning. If there are lights lighting up on the keyboard after the windows loading animation then this is probably the case.
So first thing I would check is whether or not the keyboard if USB is plugged into a standard USB 2.0 port which if your unsure you can look up your motherboard specs and determine the best ports to use for this.
USB 3.0 are the blue ones so definitely don't use those for a keyboard if there are other options.

If this is not your issue then you can always force the Bios to be a given option by unplugging your SSD temporarily from it's SATA and power plug. I would do this at the drive usually so I don't rearrange the order of my drive at the SATA ports later on when I reconnect it.
At this point it should return Operating System not found error with an option to boot to Bios... or if you have a spiffy new UEFI it may just drop you straight in depending on how it is configured.
As panathas said there are different ways to access UEFI in win8 and 10 with some systems as well. This could very well be your issue.

So first thing I would do once in the Bios is to set the options for your System Startup to be accessible more easily. Usually just switching off the Startup Splash Logo (My gigabyte 990fx has the option listed as Full Screen Logo Show under Bios Features heading and this can be either Enabled or Disabled) or whatever your option is called would be the quickest best option for this as then you can see the post routines running (however quickly) and your keyboard options hopefully will be listed on the screen as well. If yours is the newest of new UEFI's it may be you can't access Bios the old fashioned way at all. I'm not sure as I don't have any systems like this myself.

Whether or not you can see the keyboard options at post they should still be accessible unless there is some other option set in Bios blocking this. And Del would be the commonest key to perform this action usually.

In any case disconnecting your OS boot drive should get you in the door as a last resort.

Hope this helps if not tell us what it did instead.
Good luck.
-John

Catching the Bios by continually depressing the Delete key can be a hit and miss affair. however it should work if post has recognized your Keyboard. Sometimes you have to use a PS2 keyboard initially.
Some later model USB keyboards are not recognized and a Bios update is required.