Suggestions to fix white screen when booting

"A white screen is indicative of a bad hard drive. In your case it sounds like you have a fusion drive set up so it's harder to diagnose. Since you have a bootable USB device, I would start with it. Disconnect the hard drive and remove the SSD. Now see if you can boot just from the stick. If so, then install the most likely failure candidate, the hard drive and attempt a repair using Disk Utilities from the USB. Even better would be to put the suspect drive in an external enclosure.

UPDATE 8/7/17

I would really feel better about this if I knew for a certainty that that USB flash drive would completely boot on another Mac. (Then try it on the iMac with both internal drives out. That said, I've done reflows on the GPUs on this machine and the 21.5"" with about a 70% success rate. You don't need a high end hot air work station to get the job done. iFixit does not have a guide for the 27"" but does for the 21.5"" and the are going to be almost identical when it comes to the card. Here is that guide, if you decide to do the flow let me know and I'll recommend an economical hot air gun. iMac Intel 21.5"" EMC 2428 GPU Card Replacement

The video card for your 27"" machine is Apple Part # iMac & 661-5969-R

The part is not cheap. I'd like to see you try a reflow of the card before buying the card. An inexpensive station is about $100 and after use you could resell it for 3/4 of what you paid for it. http://www.ebay.com/itm/AT8586-Hot-Air-G...

What have you got to loose?"

"I just solved this issue!!!

The problem is, I've no idea how.

I've bought a second graphic card on eBay, but even with the 'new' graphic card the problem was exactly the same.

So I've unmount the motherboard again and again.

I've removed the battery of the motherboard for a few hours.

I've tried the 'old' graphic card without cooler: I just plugged it into the slot (without cooler) and without unmounting the motherboard.. and bingo.. the iMac start working again. I've really no idea why.

I plugged the graphic card 'the hard way' without a view on the slot.

May be it has moved a pin or something ... I really don't know.

I was able to remount everything correctly, with cooler and all cables, and the iMac is working again.

That's a mystery."

Have the same problem as above with my 27” 2011 iMac. Tried everything. If yhe problem is the Video Display Card, would the Apple Hardware Test confirm it?

What if you stick a Windows 10 (installed) drive in there and it boots (completely) into Windows 10 and it works perfectly and yes OSX still won't boot to anything but a white screen?