You have several choices, depending on your time and experience level with Magento and PHP.
If your time is short and need great, we use a product http://amasty.com/extended-product-grid.html and it is very helpful for a variety of functions in product management. Purchased it for $99 US and would do it again. (I'm not a part of Amasty in any way)
If you have time and interest in further learning Magento you could extend the product grid to show the field needed. Then use that field to find items via search that are out of stock and qty > 0 and mass update.
And if you have a test server all the better.
Assuming Magento 1.7.02 I tried the following, line numbers slightly modified from earlier version in this post: the last entry on the first page by "joeymetro".
1) Copy over app/code/core/Mage/Adminhtml/Block/Catalog/Product/Grid.php
This makes it more upgrade proof.
2) Edit app/code/local/Mage/Adminhtml/Block/Catalog/Product/Grid.phpnand add the code below.
After the code on line 63
$collection->joinTable( 'cataloginventory/stock_item','product_id=entity_id', array("stock_status" => "is_in_stock") )
3) Then below around line 209 after
'index' => 'price',
'header'=> 'Stock Status',
'width' => '60px',column
'index' => 'stock_status',
'type' => 'options',
'options' => array('1'=>'In Stock','0'=>'Out Of Stock'),
Save that file!
Now refresh your grid and you should see the stock status field.
First Search Stock Status = "Out of stock" and Qty From 1 ,
Next Select all
Then select the Action of Update Attributes and Press Submit.
Look in the Inventory section at the bottom and click on change then change to in Stock.. and press save. when it returns to the grid, no record will be displayed until to clear the filters!
I hope this helps.