Sorry about that
(Jessics, I really wasn't just rephrasing the question / suggestion? I agree that we are all here to help one another and by posting a suggestion in the title I was indeed trying to be helpful - the title of my post really "saying it all" - I was trying to avoid being unnecessarily verbose and most certainly not being brash.)
However, to enlarge, and help understand the purpose of my suggestion, where internet access does exist (as is confirmed by the ability to ping external addresses) failure to access internet addresses may be due either to DNS failure as originally suggested, alternatively it may be down to blocking of either DNS requests or access to specific ports by local security measures. Both antivirus and firewall software may be responsible for such blocking of either URLs and/or port numbers.
As you can ping IP addresses but not access domain names you are rightly focusing on DNS and before we start to dig into whether your ISP is assigning a working DNS to your router and whether your router is correctly forwarding requests we need first to ensure that neither your antivirus or firewall software are stopping such requests even reaching your router.
DHCP, as you probably know, works on both sides of your router but as you can ping an externall address it would seem that both address allocation from your ISP to your router and allocation between your router and pc are working ok so I think DHCP is unlikely to be the cause of any problem.