A certified HDMI cable means that it has been tested and passed the Compliance Test Specifications for the current HDMI specifications. That is your only "guarantee" that the cable you bought will meet or exceed the HDMI specifications for that length of cable. For example, a mfr can offer a certificate of compliance for their 10' HDMI cable but that doesn't mean that their 6' or 15' HDMI cables have been tested and passed CTS. If a mfr states that their cables meet the CTS, then they should be able to provide you with certificates for any length of cable they sell, not just one. HDMI 1.4 has a maximum bandwidth of 10.2 Gbps and that's what they certification should be for. If your cable is certified by and HDMI.org approved testing group for 14.4 Gbps that's fine. But the current HDMI chipsets can only handle 10.2 so that "extra" bandwidth is meaningless at this point in time. Current certified High Speed HDMI cables will be able to meet HDMI 2.0 once the CTS testing results are released so there won't be any special HDMI 2.0 cables to purchase, only cables that have meet the CTS.
You don't have to get a certified HDMI cable if you don't want to. But as I said, it is the only way to guarantee that your cable is not going to be the weak link in your system should something not work correctly. And yes, I have used Monster cables a long time ago, paid a premium price for them, got educated, and never used them again. Any mfr can have a bad cable from time to time, certified or not, but given that you have gone thru a number of cables, including Redmere, leads me to believe that there is something else affecting your system, what ever the problem is, and not the HDMI cable.