ArcMap and ArcCatalog are generally slow to open and many complain about their performance in general.
I have more less the same specs on my desktop (except I have 12GB RAM, not that it matters much since ArcGIS is a 32 bit app, and a 15,000 RPM hard drive) On this machine ArcCatalog opnes in 28 seconds the first time and in 15 seconds the second time I open it.
It seems that SDD (solid state) hard drives makes a significant difference because on my laptop with the same specs you have but with an SDD hard drive ArcCatalog opens in 12 seconds the first time and in 7 seconds the second time I open it. (Same folder connections as the desktop)
Did you try to open new ArcMap document or an existing documents containing layers and data? The speed of opening an ArcMap document is dependent on how much data you have in your document.
As for ArcCatalog, reducing the number of Folder Connections (especially those located on a network) seems to improve performance.