If nothing happens when you try to run mIRC by double-clicking on the mIRC icon then the reason could be that your mIRC files were damaged when your computer crashed. However you indicated that you installed a new version of mIRC over your current files, so that is unlikely to be the cause.
It may be that Windows itself is blocking mIRC and preventing it from running, however it's far more likely (and the following is almost always the reason) that you are using anti-virus or firewall software that is doing this. Please see my previous reply
regarding a similar issue.