First test with anything else, remove the {{block}} from the CMS block and write something in it, does it work?

If no

then you have a problem with the view of ANY block. Check your app/design/frontend/<base>/<default>/template/catalog/category/view.phtml for this entry:

<?php if($this->isContentMode()): ?>
    <?php echo $this->getCmsBlockHtml() ?>

<?php elseif($this->isMixedMode()): ?>
    <?php echo $this->getCmsBlockHtml() ?>
    <?php echo $this->getProductListHtml() ?>

<?php else: ?>
    <?php echo $this->getProductListHtml() ?>
<?php endif; ?>

If yes

Something with your block is wrong or with the template. Check the template and the system.log for errors

It isn't exactly possible to simply move the current functionality associated with the category into the left hand column, since by moving it into the left hand column you would be moving it outside the bounds of the block that renders it. That being said there are other ways to achieve it. The best approach would be by use of the 'Widget Instance' functionality in Magento.

1. Go to CMS > Widget and select Add New Widget Instance.
2. Select Type > CMS Static Block and your current theme before clicking continue.
3. Click Add Layout Update and select Anchor Categories for Display On.
4. Either select a specific category or all.
5. Select Left Column under Block Referece.
6. On the second tab Widget options select the static block you wish to inject.
7. Click Save and continue.

You may have to go clear the block cache at this point, I can't remember if that's automatic. But you should essentially have a static block in the left hand column. The main caveat being it won't appear if the templates have been modified sufficiently to remove the code for rendering them.