What's your buffer settings on your Audio Card? Raise this to like 2048 and see if it will play it back or 4096. For playback it's not such a big issue to have this latency but for recording it can cripple you.
Are all of your samples streaming from one hard drive? Your problem to me sounds like it could be related to your hard drives not keeping up. Keep in mind that when a hard drive cannot stream all that you are requesting, this translates to CPU load. Because the CPU will HAMMER the hard drives screaming give me more now! And it will do this until it hits 100% CPU. You may need to spread your samples on multiple drives to fix this (I just did this myself 1 month ago and solved all my huge score issues).
Are you running MIR PRO? Make sure your latency is also setup properly. Don't leave it at 0, make it higher according to what you choose to put your audio card at.
Sibelius is also a CPU hog, so you need to try the above to help the CPU not have to fight system resources and Sibelius at the same time so hard. See if that helps some.
Maestro2be
EDIT** - I just read your signature and you have a nice setup, including some SSD's. I would assume with all that you have running, you are also using a lot of individual EQ's etc on each channel which also adds a lot of CPU Usage. MIR PRO requires a lot of memory and CPU, but most importantly, it requires a hefty amount of "speed" from your RAM to keep up with the realism it is creating with it's reverb engine. Again, please raise your buffer on MIR PRO and your Audio Card a lot until it maybe fixes your issue. Then, begin to notch it down 1 step at a time until it hits it's threshold again. Then raise it back up to the one higher than the threshold you just hit.