Don't know about the lan card dieing, but give this a try to solve the other 'slow down' problem;
Right click 'Computer', click on Properties, then on the left side "Advanced system setting". That brings up a window titled 'system properties': click the "Advanced" tab, and under 'Performance' click Settings.
That brings up a window titled Performance Options. Click the tab 'Advanced'; go to virtual memory and click 'change'.
In this window the check box next to "Automatically manage paging file size....." should be checked: Look below and see what the "Currently allocated" amount is. It should be equal to or greater then you installed memory.
Here's what MIGHT fix your problem.
Uncheck the box for automatic; check the box for 'Custom size'. Make the initial size 8192MB (double the size of your installed RAM) and make the maximum size the same.
Click o.k. and follow the instructions for making the change permanent (think you have to restart).
See if that helps.
This controls your paging file; space used on you hdd to store stuff that the PC can't put on the RAM (very, very simple explanation). This can happen during gaming etc. Your computer will access it as needed; it is waayyyy slower than the RAM but if the paging file is too small it can give you the warnings you are getting.
If that doesn't solve the problem, try it one more time and double whatever you put in the first time. You have a huge HDD, don't worry about using to much space. If the second attempt doesn't solve the problem, then there is something else going one.