Based on the error you specified in the comment, I can conclude that you cannot use the flat product tables. It's exactly what I was saying here. You have too many attributes (or too large values) used in product listing. Edit your product attributes and change the field Used in product listing to no for the attributes that are not needed in the product list.
If they are not that many, you may want to remove from product list the product description or any other field that has long values.
[EDIT]
If you don't want to remove attributes from product listing you need to disable the flat products. The website will work a little (or a lot) slower, but at least it will work.
#6 /home/organico/public_html/app/code/local/Innoexts/AdvancedPricing/Model/Mysql4/Downloadable/Indexer/Price.php(134): Varien_Db_Adapter_Pdo_Mysql->query('INSERT INTO `ca...')
The line above means:
Check your file /home/organico/public_html/app/code/local/Innoexts/AdvancedPricing/Model/Mysql4/Downloadable/Indexer/Price.php line 134.
It does an INSERT INTO and refers to a 'date' column that doesn't exist.
If you didn't make that extension, contact the person who made it.
If you want to make sure this is indeed the extension that is the problem, disable it and re-index your products, it should work.
Best Answer
To resolve the "Cannot initialize the indexer process" you need to run follow below step
Solution 2 :-
Then clear the magento all cache and run this file as http://domain.com/reindex_custom.php