Danovak, congratulations on the Brio-r! If it came with the typical 18g cord an upgraded pc should provide positive results. If I were you I'd spend a few weeks with the stock cord and then try others.
With my Arcam FMJ A19 I first tried a shielded 14g Belden. There was an immediate improvement in bass and dynamics. The sound was still a bit flat, hard and veiled. I then put a WireWorld Stratus on it. A very good improvement! Dynamics, tone, timbre, detail and resolution all improved and the background was quieter and blacker.
It was a great upgrade for a very reasonable cost. Also, I read somewhere that Rega was offering an upgraded power cord for the Brio-r as well.