A layered method
The web page will not load. Rather than guess, check one layer at a time from the bottom: the physical link, the IP address and gateway, DNS (names), then the service itself. Each layer needs every layer below it to work.
First the physical link: is the cable plugged in with its link light on, or is the Wi-Fi joined? With no link, no packet can leave the laptop, and nothing above it can work.
Next: does the laptop have an IP address and a default gateway (the router that leads off the LAN)? Here it has 192.168.1.10/24 and gateway 192.168.1.1. An address starting 169.254 would mean DHCP never answered.
Ping
Ping sends an ICMP Echo Request (ICMP carries the internet's control messages) and waits for an Echo Reply. The gateway 192.168.1.1 answers in about 1 ms: the round-trip time, or RTT. The home network works.
Now ping the server by address, 203.0.113.10. The reply takes 25 ms and arrives with TTL (time to live, a hop counter) 61: it left at 64, and 3 routers each took one off. The internet path works.
Ping by name: ping www.example.com first asks the DNS server, here the router, for the address. It answers 203.0.113.10, so DNS works. Had the address ping worked but this failed, the fault would be DNS.
Ping only proves the machine is reachable. The page needs the web service on port 443, so the laptop tries a TCP connection. The server answers RST: nothing listens there. Found it: the network is fine, the web server is down.
Traceroute
When ping fails, traceroute shows where. Its first probes carry TTL 1. The router takes TTL down to 0, must drop the packet, and sends back an ICMP Time Exceeded message from its own address, 192.168.1.1. That is hop 1.
TTL 2 dies at ISP router A, TTL 3 at ISP router B. Each sends Time Exceeded from its own address, and traceroute times every answer. The list of addresses is the path, and a big jump in time points to a slow link.
TTL 4 is enough: the probe reaches the server with TTL 1 left, and the server answers with an Echo Reply. Traceroute stops. Had the answers stopped at some hop instead, the break would be just after it.
Packet capture
A packet capture tool such as Wireshark records every frame the network card sends and receives, field by field. It shows the SYN leaving and the RST coming back: proof to hand to whoever runs the server.
Commands and packets, field by field
;; step 1/11 · work-up-layers · local ;; at laptop symptom: https://www.example.com does not load check bottom up, stop at the first layer that fails: 1 Physical link link light / Wi-Fi joined 2 IP address + gateway address, ping the gateway 3 DNS name → address 4 The service TCP to port 443 a fault low down breaks everything above it, so a working higher layer proves the lower ones work
Each router answers from the address of the interface that faces you, so traceroute shows those addresses. Traceroute sends three probes per TTL; the figure shows one. Some routers and servers do not answer ping or traceroute probes at all. A row of * * * or a silent ping only means no answer came back, not that the path is broken.