If it's 4 years old, chances are the primary bearing in the drive has failed. This is not good, but there is still a slim hope and a few things to try that might work.
First up, the freezer trick. The bearing in the drive has likely failed, and extra friction is probably causing the drive to not be able to spin up. If you are very lucky, you can place the entire drive assembly in a sealed plastic bag (to prevent condensation reaching the drive) and place the unit in the freezer for about an hour. Then, immidiatly take the drive out of the freezer and plug it in and see if you can read any data. This will either work, or it won't, and it is a temporary fix only, so immidiatly start copying the most irriplaceable data off the drive to the computer. Once it heats up to the point it fails again, you are probably done.
If that doesn't do it, you can try the strike trick. Only attempt this after the freezer trick. Take the drive out of the external enclosure, turn it upside down, and then pick it up about 4 inches on a hard surface and drop it down hard. the theory is that this will knock what was the bottom bearing bearing loose and force the drive to use the top bearing. It doesn't always work. Put the drive back together, try the freezer trick again if you like, then turn it on and see what happens.
If that doesn't work, your only real remaining option is a drive platter swap. It is theoretically possible tyo do this yourself, I've never been successful attempting it personally though. Your best option at that point is weighing the importance of the data vs. the $ thousand or so it will take to have someone swap the platters professionally. (something like this company for example: http://www.krollontrack.com/data-recovery/data-recovery-services/hard-drive-recovery/).
The process is simple enough. You get an identical drive to whatever is in the enclosure (numbers matching all the way) and pull the platters out of that one, then transfer the platters from the dead one into the working one. The problems come that if you even touch that platter with a finger, get any dust on it, etc, chances are you have just ruined your data. It's very expensive, but your chances of a successful recovery are orders of magnitude higher with a professional recovery company.
Now, on to future backup proofing your computer
You had a good theory, but there are a couple things you can improve upon for the future. First off, you need an external enclosure that has two drives inside it in a "Raid 1" mirrored configuration. This means that every single file you write to that drive goes to both of the drives inside. For example, you install 2 2TB drives, they show up in the system as 1 2TB drive, but if one of those drives ever fails, you still have all your data on the other drive. I use personally the Netgear Readynas Duo. (http://www.newegg.com/Product/Product.aspx?Item=N82E16822122098
for $199, plus two identical hard drives in addition). If you also happen to have a desktop computer, I'd strongly urge you to consider also installing an internal data drive, prefferably in a raid 1 mirror as well if your motherboard supports it, and then set up automatic backups between both drives. The theory is that hard drives WILL fail. it's only a matter of time and conditions. the more places you have your data, the better. You also may want to consider setting up an online file storage repository at least for the important files that aren't necessarily confidential (your pictures and music yes, check stubs and financials, i'd not put online)
Finally, i'd also reccommend you purchase a $79 blueray burner and some 60GB blueray disks, burn all your records to disk, and lock them away at some other site, prefferably in a safe or a safe deposit box. I actually have an exchange program set up with my family, they host copies of my data (my in progress novel, etc) and I hold copies of theirs here.
You can't be too paranoid about data backups. Good luck with your recovery efforts. If you want more backup pointers for the future, either ask us or take a look at part two of the stickied computer health guide I wrote.