I have a Mad Dog hard drive enclosure that I did have a Western Digital WD400 hard drive in. Now I need to recover some data from a Western Digital WD1600. The ribbin that connected to the hard drive is different. Is there anything I can do to use this enclosure?

Mad Dog is, unfortunately, out of business by all indications and there is no support available from them. I suspect that Windows 7 will not have a driver that is compatible with the enclosure's interface. Depending upon what brand/model of actual hard drive is inside the enclosure (Western Digital, Seagate, whatever) you may be able to dismantle the enclosure, remove the actual disk drive, and use it in another enclosure with an up-to-date interface. That is only a suggestion...it would require a certain amount of mechanical expertise and a good phillips screwdriver ;-)

Depending on the exact failure, you have a couple of options. A friend of mine had a similar drive with important photos an it turned out the drive itself was OK, the enclosure had failed. I removed the drive from the enclosure, and connected it to another system with a drive adapter, and recovered the data.
If the actual HDD in the enclosure failed, you can contact a data recovery company like www.drivesavers.com and get an estimate on data recovery (Generally very expensive, just depends on the importance of the data)

Is this a hard drive or an optical drive? The model under which it is listed implies that it is a internal DVD drive.
If, in fact, it is a hard drive (fixed platter(s)), you might consider buying SpinRite from Gibson Research. I have recovered data from many drives over the years with it that were considered 'dead.'
SpinRite

Sometimes the drives pull too much current to start. I understand that it worked in the other caes, but the electronics in this case may be pulling more.

Usually they come with a two-headed USB connector. Try putting the single end in the drive and use two USB ports on the other end. This doubles the current available to the drive.

If the hard drive does not even turn on, then check its power supply. Maybe the power supply went bad; it should be a standard 12V 3.5A power supply.

Even if the power supply is working, chances are good that your data are still there, because the unit not turning on means that the internal enclosure, not the disk electronics, got messed up. It's unlikely that BOTH enclosure electronics AND disk electronics went south together, unless you got a lightning strike at short distance (less than 60 feet, say). You'll need to open the enclosure, extract the drive and connect it to another compatible enclosure (most USB/eSATA enclosures with the same EIDE or SATA connector as your WD will do) in order to override the fritzed enclosure electronics and connect directly to the hard disk. Once you do, your data will be there. If the disk crashed last time it turned on, maybe you'll need to run disk checker and expect to lose a file or two.

On the other hand, if the drive does turn on when powered, and the PC "just" doesn't see it, chances are proportionately bad for your data: you'll need to send the disk to a data recovery service, which can be quite costly.

Purchased a USB to IDE cable. Looked like it was communicating with the hard drive (WD400) my computer did not see the drive. (Vista OS).

Western Digital customer service recommended that I change the jumper pin to position #4 on the hard drive and install inside the computer as a an additional slave drive.

Worked perfectly.

It seems like the mother board for the enclosure has failed.
Normally for external hard drives, you could just remove the drive from its enclosure, and place inside another enclosure, but for this type of drive, that's not possible due to the linux os partitioning of the drive, and the mionet requirement for the data.
As these drives come with a 3 year warranty, your best optin is to create an RMA on the Western Digital website http://support.wdc.com/warranty/index_end.asp?lang=en and choose the option to have a new drive sent out prior to sending the old one back.
When the new one arrives, open both enclosures, and swap the hard drives. This should enable you to recover the data.
Do ensure you send the old enclosure back wiyhin the 30-day limit, or you will be charged for the drive.

This may sound silly, but does the external enclosure have power? You may have neglected to connect the required power adapter, or it may not be working properly. You might also have a problem with the enclosure's internal power or data cables. They are sometimes pretty flimsy, and sometimes they can go bad.

There's also the chance the drive itself is bad and isn't being detected as a result. Or the interface board in the external enclosure may have failed, and the drive is OK but the computer doesn't see it. If you are connecting to a desktop PC, you can try connecting the drive directly to the main board using an IDE cable and try accessing it that way. Just be sure to set the master/slave jumper accordingly if you do that.

Does you drive make any sounds like these? If yes you have a mechanical problem and you should get a specialist to work on it.
If not - try to remove the drive from the enclosure and connect it directly to the computer to recover your files.