Hi
You are stating that you want to connect to a VirtualBox virtual machine and that this machine is running as a guest machine inside of your machine, please correct me if I have misunderstood that part. As for the remote connectivity to the guest operating
system, I understand that you would like to establish a remote connection from the host machine in to the VM, is that correctly understood?
Absolutely! You understand the case quite perfectly.
But as I stated previously:
>> Take a look at the VRDP
manual on the Vbox site. VRDP server is functioning on the host machine regardless of the
guest machine installed (Windows, Linux or other). In my particular case it's Linux Mint.
There is absolutely no matter which guest OS is installed.
>> When connecting to the Linux VM, has port 4444 on the VirtualBox VRDP Configuration worked before the system reinstall?
Yes.
>> If so, did you also do any configuration changes to the Microsoft RDP client in order to
connect to the port 4444 instead of the standard RDP port TCP 3389?
No. How do you think could I change standard MS client if I even didn't know how to see its logs till this moment?
I specify port like this

Like usual. Without any hidden configurations.
>> Have
you tried changing the port configuration on the VirtualBox configuration?
Yes. Nothing changed. I've got the same error.
>> I
would also like to present the possibility of migrating the virtual machine in question to utilizing the built in Client Hyper-V role of Windows 8.1
Could be-could be, but I have no Hyper-V option in Windows functions activation. Maybe it's PRO-feature?
Nevertheless, I'm waiting for analyse results of my logs.