The Time Machine Preferences Panel tells me it is set to make a back-up the following hour, but when I enter TM, there is only one backup for every day unless I prompted "Back up now."
What are your sleep settings? Time Machine will not back up while your computer is asleep (or off). (If it missed a backup because it was asleep, it will start one two minutes after you wake it up. If it was turned off, it won't start making automatic backups until one hour after you turn it back on. If you never leave it on for a whole hour, it'll never back up except manually.)
When Time Machine was new, there were a lot of hacks in circulation to let people "tune" TM. Some people were so sure that hourly backups were surely a bad idea that they insisted on finding some way to make TM back up only daily or even less often. Is it possible you ran one of these at some time in the past?
One quick check is to run the following command in Terminal:
defaults read /System/Library/LaunchDaemons/com.apple.backupd-auto | grep Interval
Depending on your OS version, the output should be either:
StartInterval = 3600or
Interval = 3600(preceded by a bunch of spaces). If it's any number other than 3600, somebody has messed with the frequency of automatic backups.
later on I noticed the backups of the oldest drive only contains the user folder, which is good to have, but the rest is gone.
When TM was new, Apple gave users easy access to an option to not back up system files. That option was a mistake, and Apple removed it in later versions. You really do want to back up your system files. Otherwise, you cannot meaningfully do a full-disk restore. System files rarely change, so even though they're big in aggregate, they don't take up as much of your precious backup disk space as one might naively fear.
You probably had that option on in the beginning, and then turned it off. The default (and correct) option is to back up system files.
I feel like it may be time to just wipe the TM drive and start over like I did when I couldn't resolve the problem with the internal drive and it was the only solution I could come up with. I don't know if TM kinda starts a new file (not folder) when you wipe a drive and start over because there are so many changes trying to figure them out would be 'nuts.' Just kind of start fresh without artifacts of anything. Really can't imagine a case scenario where something probably corrupt from years ago is worth keeping or fixing. What say you?
Yes, when you wipe a drive, TM sees it as a brand new drive and starts a new backup for it. (On OS X 10.7 Lion and later, there is a Terminal command to tell it to adopt a new drive as a reincarnation of a previously backed up drive, but you have to do that manually. There was a very complicated procedure, not for the faint of heart, to accomplish the same thing in OS X 10.5 Leopard. You cannot do it at all in OS X 10.6 Snow Leopard.)
It's sounding more and more like what you want to do is start TM fresh on a newly-erased drive. Either buy a new drive, or erase the existing one. It doesn't sound like you'll be losing anything important if you do the latter. Do not waste time trying to futz around and trash just some of it. Erase the whole drive. (If you start with a new drive, don't forget to set the partitioning scheme to GUID.)
