Router will not see modem

sometimes you have to reboot the router and the modem in different orders, try rebooting the modem first, then the router, while the router is unplugged.

If you have a separate modem and router turn both off and reboot only modem till all lights up the reboot router till all lights up in that order sounds simple communication problem between router and modem. If router modem combo unit disconnect either dsl or cable from router/modem leave diconnected for a short time then reconnect and reboot till all lights up. Hope this helps.

try to connect directly to ISP modem (without router)

First of all, can you confirm that you get internet access continuously when connected to the Modem directly? If No, I would suggest you talk to the ISP else lets try the steps below, .
So try power cycling the entire setup
1. Power off your modem 2. Power off your router
Now Switch on your modem, leave it for a minute and then switch on the router. Usually a power drain will help. I noticed that you have been switching off your router several times. Lets try this once
Alternatively, I would suggest you reset the router once and set it up again.

the modem recognizes your main computer and not your router.
power cycle the modem to make it recongnize your modem.

When you say your rebooted the modem and router, do you mean you power cycled them both? If you're unfamiliar with power cycling, this the technique:
1) Unplug your main Cable or DSL line from your modem.
2) Unplug the power from the modem.
3) Unplug the power from the router.
4) Wait about 20 seconds.
5) Plug the Cable or DSL line into the modem.
6) Plug the power into the modem.
7) Plug the power into the router.

Make sure that all computers are shut down and completely off. After you have power cycled, reboot the computer(s). If you still do not see the SSID (the name of the network), then someone probably hacked into your router and changed the password. Here's how to overcome that:

1) Unplug the power from the router.
2) Press and hold the Reset button on the router for at least 30 seconds.

3) Plug the power into the router.
4) Open an internet browser (Internet Explorer, Firefox, etc.).
5) Type in the IP address of your router. For this router the IP address should be 192.168.0.1
6) You should be at a login window. The User Name is admin and leave the password blank.
7) You should now be in your router's configuration options. You should enable the highest security possible, then change the default User Name and Password to something secure, with letters and numbers.

My information for you router came from this link:

http://www.myacrobatpdf.com/8429/dlink-wireless-router-dl-524-setup-instructions.html

When facing the router, Globe/Internet LED is on the right. Below are the LED indicators; Check the steps below:

Wireless Security - This light will only turn on if the wireless security is enabled.

Wireless-Computer Status - This light will turn on if a wireless computer is connected to the router.

Wired-computer Status - This light will turn on if a wired computer is connected to the router. Connect the wired computer to any gray port on the router. (There are 4 gray ports).

Router Status - Power light. Solid blue means the router is on and ready.

Modem Status - If this is off, it means the router is not connected to the modem. Make sure the cable is connected from the modem to the yellow port on the router.

Internet Status - This light will indicate if the router is connected to the internet.

If this is the first time you are installing the router, then what is important is to get the router, wired-computer and modem lights ON. Once they are on, you may insert the CD that came with the Belkin router to setup the internet connection and wireless settings.

First unplug your router, then unplug your modem and for 10 seconds. Next plug the modem back in and wait it to reboot(on mine this a series of 4 lights that light up in sequence, when the 4th light stops flashing, reboot is complete). Finally plug your router back in.

If its solid red its possible that there is something wrong either with the firmware of the device or it's already faulty. Aside from rebooting your router, you can also reset it for 15-20 sec and check if the power light will be green again. Doing the reset will erase all of the setting you have set on the router. In case after a couple of reset and the router still has a red power light then you can call your router manufacturer if they have other options or if you really need to get a new router.