I'm sure the drive is okay. I say this because many of us are experiencing Time Machine issues. The smartest among us say it's hardware and the consumer and I say it's a Perfect Storm that wreaks havoc on my nerves each time it happens.
The general consensus, in many cases is the same for everyone; unplug everything • wait • restart. Odds are your drive will begin behaving properly once more. That is, until something else happens with the TM system.
Apple has produced myriad White letters addressing these issues and we rely on the most vocal members of this site to glean the salient points and rewrite those statements all-day-everyday.
Your issue, the drive is too full is something I experienced. I added a second drive thinking I was chaining two TM drives BUT the "System" could not get TM to recognize the first drive, once I added the second. wow.
I tried for a day and just abandoned the first drive. The second drive is now the primary one. We work to solve our own problems but in many cases things suddenly start working again and you're never sure which solution worked!
On the July 1st, I finally used the first drive to restore my Mac back to Lion and was relieved to see the drive perform flawlessly. Although TM was behaving just as erratically and more importantly, inconsistently, on Lion, it seems ML came with a whole new slew of issues that are so un-Apple-like, I've decided to stick with Lion until I get a newer Mac.
There's a lot of good information on this web site and many brilliant minds to assist you. What you should be mindful of is, being very specific about the nature of your problem.
You have to help those helping you by giving them names, dates, models, and logs if you know how to get at them; the Logs are your insight into the soul of your Macintosh; everything is recorded and well documented and like many fine Apple products, there's a decent interface to all of that information and it's called Console.
Type Console into Spotlight and hit Return and you'll be absolutely amazed at the volume of information your Mac is collecting, regarding its health and current state. The left-hand column is an Index of sorts. Applications like iTunes and QMaster keep good records of every query; issues and resolutions, that will ultimately lead to well-informed decisions regarding the state of your Macintosh.
For example, I use ClamXavSentry to monitor my Downloads and Desktop folders and ClamX produces a log into which every file I bring into my Mac is scanned for anomalies and blessed with an OK and I can read it all from Console.
These logs provide valuable forensic information and in all cases, you can actually cut & paste data from these logs into your comments, which can lead to an expeditious conclusion. Conduct a search for Apple White Papers regarding Console and its Logs and commit to learning a little more about what goes on behind Apple's consumer interface. Information is power.