Intel HD Graphics not detected, advice?

[Norinion]

Intel HD Graphics not detected in Device Manager when a dedicated graphics card is plugged in. (I need the Intel HD Graphics are other features)

Solutions I've tried:
1. Unplugged Dedicated Graphics Card (DGC), the Intel HD Graphics was detected and working fine. Drivers updated, plugged back in DGC then I'm back to square one.
2. Read somewhere it's a BIOS feature. Looked in my BIOS (pic 1, pic 2), and the feature doesn't exist. Updated BIOS, rechecked, same issue.

My Setup:
Gateway DX4860
Motherboard: Stock
Processor: Stock (i5-3450)
RAM: Upgraded (16 GB)
Graphics: Added (ATI Radeon HD 7850)
OS: Windows 10 (current, but 7/8/8.1 had same issue)

Questions: Is there another method? Or around the BIOS issue?
If not, can I just buy another compatible motherboard to replace it (without replacing the CPU) and reinstall a fresh OS?

Thank you!

Additional Info:

Spoiler

Reason I need it working: I recently got a new Samsung TV with a MiraCast feature. But in order to MiraCast to the TV, I need to send a wireless display signal over to the TV. The "Cast to"/"Play to" feature works, but the MiraCast however doesn't.

I also wanted to enable the Hardware Accelerated Decoding/Encoding on Air Video Server HD, but need the Intel HD Graphics feature working (as stated here).

I'm also running 3 monitors, all 3 connected to the GPU, but 1 is running an Active DP adapter. The one running the Active DP adapter isn't showing proper colors (as seen here), and would love to use the integrated graphics card for the 3rd monitor to fix this issue.

Under Device Manager>Display adapters, I only see AMD Radeon HD 7800 Series, while other computers, like my brother's (different model and build), would have both their dedicated and integrated graphics card detected.

 

[rgd1101]

Unless the motherboard offer duel monitor feature with iGPU/dGPU, it one or the other.