If it only checks FD, that is lame application of the product, but I guess it could be that limited. Put FD back to original in my edited files then, this is easy edit at line 60 in hex on full file.

5MB ME is not required for the CPU, so that's not the reason they would use the 5MB ME, but it could be related There could be some TDP limit/lock in there, but I bet some kind of CPU allow/disallow list
Often CPU compatibility has to do with ME and microcodes, that's why I started there, but this is not always the only things. The BIOS you linked above have microcode we have not tried yet, we could try those next instead (leaving ME as it is)

What should I do?
ME is disabled (MeAltDisable bit), I think there were not ME problem.
How to check CPU blacklist by BIOS?
I can't find any info on Google ;)
I read donovan6000 blog many years ago and I have IDA Pro, i cracked oldest BIOS Advanced TAB, but I don't know what should I search, and in which module ;)

There was first BIOS without RSA signing for my laptop:
ftp://ftp.hp.com/pub/softpaq/sp57501-58000/sp57981.html

Microcodes were updated and on your BIOS with i7 recovery procedure not starting, starts only with i3.
I think it may be to strong CPU.

I figured there was difference of cache size between i7-3610QM (6MB). It works with G6 2323sw, I saw that in auction portal archive listing, originally this model has i3 like mine.
The cache of i7-3820QM is 8MB.
Do you think it may be source of incompatibility?

CPU is not too strong, it's just locked out, either by CPU allow/disallow list or some other list like that in BIOS, or by a TDP lock limit. Don't disable ME, it will be required and may need to be a certain version as mentioned
the only thing I can think of left to try is the other microcodes as I mentioned.

I can make two BIOS from your link above on non-RSA signed BIOS. One w/ latest microcode and other with ones from BIOS on post #13, leaving ME as it is or update to 8.1 at least (No need to disable)
But the link does not work, so please relink that file, or download it and send me the exe

No, I don't think cache matters. In this case, I believe only ME and microcode matter, if there is not a lock list of CPU's by name/series, or a TDP lock.

I see a CPU "Energy Read" Setting in BIOS enabled, in thermal config page, maybe disable this would help. You may need to flash mod BIOS with Advanced menu enabled, it's set standard now but full access, may need advanced + Full
I also see all these settings for TDP

The CPU has broken iGPU... It runs perfectly on motherboard which won't run iGPU (HP 8470p with AMD discrete). I'm waiting for board in good price and I will attach image after buying of MB in good price ;)