To find the reason why a PC is playing up you need to start narrowing down the problem.
Am I right in saying that internet explorer closes with this error and the PC carries on working without a problem? If this is the case then the first thing to try is reset you internet explorer settings. You will find this in Tools>Internet options>Advanced>Reset. This fixes toolbar and addon related issues and a few others. Be aware though you toolbars and all internet explorer settings will go.
If this doesn't fix it then it could be malware/spyware/virus related.
If you know your way around a PC then you could download and run HiJackThis any items that could be effecting IE. BUT ONLY IF YOU KNOW WHAT YOU ARE DOING! The other options are run some cleanup software like: combofix, mailwarebytes antimalware, superantispyware, spybot search and destroy, and NOD32. These are all free downloads apart from NOD but be aware that there are software out there that are similar but not the same as those mentioned(if it asks for money, its the wrong one).
A workaround is to turn off memory protection in IE. Click on Tools, Internet Options, then the Advanced tab. Scroll down to Security and uncheck "Enable memory protection to help mitigate online attacks".
I've fixed this problem on a number of PC's but unfortunately the cure has been different on all of them, hense the various options I've given. Its a memory access issue and with IE8 trying to be very secure giving this error. The way I see it is thats fine for IE but every other peice of software that interacts with IE has to be equally well written and abid by the same memory related rules.
All this information is my own personal opinion and you should make your own mind up as to which route to take, but hope it helps.