This is what I see in the first dmesg:
ata1.00 = link down
ata2.00 = 6Gb/sec = WD60EFRX = /dev/sda
ata3.00 = 3Gb/sec = Samsung 840 = /dev/sdb
ata3.01 = 3Gb/sec = ST3000DM001 = /dev/sdc
ata4.00 = fail to resume link / link down
ata4.01 = fail to resume link / link down
ata5.00 = 3Gb/sec = WD60EFRX = /dev/sdd
ata6.00 = 3Gb/sec = WD40EFRX = /dev/sde
This is what I see in the second dmesg:
ata1.00 = link down
ata2.00 = link down
ata3.00 = 6Gb/sec = Samsung 840 = /dev/sda
ata3.01 = 3Gb/sec = ST3000DM001 = /dev/sdb
ata4.00 = failed to resume link / link down
ata4.01 = failed to resume link / link down
ata5.00 = link down
ata6.00 = 3Gb/sec = WD60EFRX = /dev/sdc
I'd start by updating the BIOS/firmware on whatever kind of x86 device it is you're using .. including any third-party SATA controller cards and check that everything is set to allow 6Gb/sec operation - I can see several drives that flip between the two which either indicates bad settings or bad cables or an insufficient power supply. Check the cables and jumper settings on drives. Then i'd start rebuilding with the SSD and get that on a 6Gb/sec channel. Then I'd add the two 6TB drives and ensure those come up. Then i'd add the 4TB .. then 3TB.
As a general comment: each time I see someone struggle with cables/connectors and drives like this I think "get a NAS box" .. because media collections are so much easier when you make the HTPC a dumb/simple/cheap client device and use a decent NAS for storage.