check taskmgr and see if iexplorer.exe and/or chrome.exe is already running when you're trying to launch them... if so end the processes (iexplorer.exe , chrome.exe) and try to launch them...
If this is the case (or even if this isn't the case) I would scan with malwarebytes or something comparable. If web browsers are running in the background on their own you should do some system scanning/cleaning