Troubleshoot Internet Connection

1. Make sure you can connect to your router by ping to your router IP (for example: 192.168.1.1) from command line (Windows) or terminal (Mac or Linux) or access to the router web page using the browser. If you cannot ping or see the router web page, check your network configuration on your computer.
2. Are you using the wireless? If yes, connect the CAT 5 Ethernet cable connect to your computer.
3. Is the wired connection working? If yes, your wireless has issue.
4. If the wired connection is not working, is other computer in your home, your office or your LAN can access to the Internet? If just only your computer, check your network configuration.
5. If all computers in your LAN could not access to the Internet, power down both the router and cable modem.
6. Wait for 15 seconds, and turn them on.
7. If you still not connect, check to see there is outage in your area. If not, verify your router is working.
8. To verify your router is in good condition, hook up another spare router or your computer directly to the cable modem. Note: If you hook up your computer directly to the cable modem, make sure the firewall on computer enable and all ports other than 80 are closed. Connect computer with open ports: 20, 21, 139, 3389 directly to cable modem or Internet is dangerous and not recommend. Here, I'm using my test computer running GNU Linux with all closed ports to connect directly to the router.
9. If you can connect to the Internet without router or with another router for an hour or more, your existing router is bad. It need a replacement.
10. If you cannot connect to the internet, chance is your cable modem or the link from cable modem to your internet service provider have issue, call your internet service provide technical support.

Compare 3G, 4G,Wi-Fi, WiMAX, and Ethernet (Wired)

Summary from Wikipedia and other places in internet:

3G is a generation of standards for mobile phones and mobile telecommunications services fulfilling specifications by the International Telecommunication Union. Application services include wide-area wireless voice telephone, mobile Internet access, video calls and mobile TV, all in a mobile environment.

4G is the fourth generation of cellular wireless standards. It is a successor to 3G and 2G families of standards. A 4G system is expected to provide a comprehensive and secure all-IP based solution where facilities such as ultra-broadband (giga-bit speed such as 1000+ MiB/s) Internet access, IP telephony, gaming services, and streamed multimedia may be provided to users.

Wi-Fi is a trademark of the Wi-Fi Alliance. It is not a technical term. However, the Alliance has generally enforced its use to describe only a narrow range of connectivity technologies including wireless local area network (WLAN) based on the IEEE 802.11 standards, device to device connectivity.

WiMAX (Worldwide Interoperability for Microwave Access) is a telecommunications protocol that provides fixed and fully mobile Internet access. The current WiMAX revision provides up to 40 Mbit/s with the IEEE 802.16m update expected to offer up to 1 Gbit/s fixed speeds.

Ethernet is a family of frame-based computer networking technologies for local area networks (LANs).  Ethernet is standardized as IEEE 802.3. The combination of the twisted pair versions of Ethernet for connecting end systems to the network, along with the fiber optic versions for site backbones, is the most widespread wired LAN technology. It has been used from around 1980 to the present.

Data transfer rates in order from low to high speed:

• 3G:  128Kbps to 384Kbps
• 10BASE-T Ethernet (Wired) 802.3: 10Mbps
• Wi-Fi 802.11b: 11MBps (Max)
• Wi-Fi 802.11g: 54MBps (Max)
• 100BASE-T Fast Ethernet (Wired) 802.3u: 100 Mbps
• Wi-Fi 802.11n: 300MBps  (Max)
• 4G: 100Mbps (mobile) to 1GBps (fixed)
• WiMax 802.16m: 40Mbps to 1Gbps
• 1000BASE-T Fast Ethernet (Wired) 802.3: 1GBps

4G and Wi-Fi have almost the same bandwidth. The difference between them is in range. Wi-Fi is targeted to cover low range networks, while 4G was designed to replace high range mobile networks.