Personally, I would use your PC exactly as if there are no longer any problems. It is natural that you received the dreaded message the first time you 'booted' after changing the router, because your comp had to re-establish the Internet connection; but everything now appears to have corrected, after your having hit 'Try Again'.
I am Not a believer in leaving a PC/Laptop on continuously, no more than I would leave my car's engine in a perpetual state of unrest.
Looking forward to your next up-date.........Al.