HP Pro 3300 & 3400 (H61): Upgrade to Ivy Bridge

[CptnIX]

I recently bought a HP Pro 3300 MT, because it was a good deal, and I still had an i5-2300 laying about. The thing is, the computer boots, but only by pressing F1 during the boot-up, will it actually start the OS. If I don't press F1, it will say that the processer is unsupported, and shut down.
Things I found out and have tried:
The i5-2300 is actually on the supported processor list supplied by HP.
I updated the BIOS to version 7.16 (downloaded from HP Support)
I updated the BIOS to version 7.16A (downloaded from this thread: https://www.bios-mods.com/forum/Thread-R...Unlock-Mod)
The BIOS chip on my motherboard is the 4MB version
Further information: OS is Win10 Pro 64 bit.
If there's anything else required to figure this one out, let me know, and I'll try to do it. I'm a complete newb when it comes to the ins and outs of BIOS, but I'm always willing to learn.
I even went so far as to download the BiosTools.zip from this website, but I'm kinda lost. What do I try next?
Is there a way to add the code to the BIOS to accept the i5-2300, or is that impossible?

[DeathBringer]

If I don't press F1, it will say that the processer is unsupported, and shut down.

Post a photo of the screen with this message.

[CptnIX]

If I don't press F1, it will say that the processer is unsupported, and shut down.

Post a photo of the screen with this message.

Here's the picture, but I'm afraid it's in Dutch, so I don't think it'll be of much use to you.
Is there any particular item you're looking for?

[DeathBringer]

I need in English.

[CptnIX]

I need in English.

Type of processor:
Speed of processor:
L1/L2/L3 Size of cache:
Memory size
Channel A:
Channel B:
BIOS Revision/Date: v7.16 03/23/2012

Error: Unsupported CPU installed
The PC will be shut down automatically in a few seconds

EDIT: Added picture of the notification in English.
EDIT2: Apparently I'm still on version 7.16 of the BIOS, never noticed that.
I tried flashing that version 7.16A, but it will not flash, I keep getting this error: "46 error: problem getting flash information"
Could it be that part of the BIOS is write protected, so that I can only flash part of it? If so, would anybody know which part I need to edit for the PC to accept my i5-2300 without issues?

[DeathBringer]

Attach TXT-report of CPU-Z with your i5-2300 (F1 bypass).

[CptnIX]

Attach TXT-report of CPU-Z with your i5-2300 (F1 bypass).

Attached.

[DeathBringer]

Try to flash my mod.

[CptnIX]

Try to flash my mod.

Tried that, using both AFUWIN and AFUDOS. Keep getting this: "46 - Error: Problem getting flash information."

[DeathBringer]

1. Download sp58264.exe
   
2. Unpack it by WinRAR
   
3. Replace CUP_716.ROM with modded version
   
4. Run command line in Windows with administrative rights and run:
   cd (full path)\sp58264
   SAFUWIN CUP_716.ROM /p /b /n /r /q