the volume icon disappears. At least, I have seen similar myself.
That SplashLite media player has its own volume control on the software window itself, and I am betting it 'takes over' the system volume control when it is running. I use the VLC Player and on my system it causes a strange effect. When it is running, sometimes I cannot change the volume from my own volume control icon. The icon is visible but moving the slider has no effect. I can still use keyboard keys to adjust the volume, or use the player's own slider. But then other times there is no strange effect.
When you have finished using your player, does it shutdown completely, or is it still open in the background? You could check this in the Task Manager, (right click the Taskbar, select Task Manager, then open the Processes tab). Use that to look for any SplashLight entries after you have closed it down. if you find any then perhaps it still has control of your volume icon.
I can also explain why your system runs smoother without those corrupted files. Windows uses "Explorer" extensively. Not just Internet Explorer, but My Computer, My Documents, Download folder and even the display on your monitor is Explorer. Explorer doesn't like corrupted files and it struggles when it comes across any. Deleting those downloaded files clears that problem if they are corrupted.