Motorola SB5100, SB5101 or the SB5120 is what I would go with. The 5100 has been discontinued but can still be found. The 5100 and 5101 have a Broadcom chipset/processor while the 5120 has a Texas Instrument chipset/processor. Some feel the TI chipset is more sensitive to noise then the Broadcom which can cause connection drops. I have heard that firmware updates have pretty much solved this problem now. I will give honorable mention to the Linksys BEFCMU10 v4 as performance is about the same as the SB's I mentioned. I have had a SB4200 for about 6 years and it still works great.
If the Cable light never goes steady then there is a serious problem with your CATV feed, or something on the ISP's end is not working. Check that your CATV cable is properly screwed into the back of the cable modem and wherever the other end is plugged into. Seems like the modem tried to sync but during registration something on the ISP's end failed or maybe noise on the line messed it up so the modem quit trying. If the modem has a reset hole on the back that you push a pin or toothpick into then try that or unplug modem then plug back in to see if it will sync all the way.
Before buying a new one you may want to check your ISP's site to see if they have a list of approved modems. For example, I have Comcast and they have a list of approved modems you can use on their network.