Can you show a (readable) screenshot of that "connection error" ? I just want to know how that message looks like, because I've never heard of it. Meanwhile tell us when that message occurs (you click "this" and after about x seconds "that" happens etc.).
On switching on the Audio PC I am unable to connect to the Music Server
Is that a bit of mis-phrasing ?
If the music server is your remote control then you should say "can't connect to the Audio PC". Not nit picking, but possibly it is an indication of doing things we don't expect.
Lastly, your static IP address is - at least to me - something unknown. Ok, I know what it is of course, but I don't use (it like) that. To be sure it's not the culprit I'd switch this off (take it out).
Of course you must again obtain the IP address and feed that to the RDC program on the remote, but it could be worth the trial. I myself really have no other options in mind why it would not work, and FYI the same Audio PC worked without video card over here.
Oh, if you changed something in the BIOS then obviously it could be that (not that I would know exactly what, but I am confident it can matter (UEFI vs BIOS stuff).