Checkout Error – Fix 500 Internal Server Error Redirecting to Shopping Cart

I am new to Magento and this is my first project.

I am using Magento CE 1.9 I have made all the set up required. Now when I try to test by creating an order I face an issue in last step :

When I click on the "Place Order" button, it goes back to "Shopping Cart" page.

I also noticed that though the order is not placed, stock is getting reduced!

With a little bit of debugging, I understood that if there is any "failure" in Ajax requests (I use Magento's standard OnepageCheckout), it will get redirected to "checkout/cart" page.

I can see that all the details are entered – billing and shipping address, shipping method, payment method (Cash On Delivery).

In the browser console I see the error – "500 internal server error".
What does this actually mean? I am testing using a logged in customer.

This is the first order I am trying to place. I really appreciate an suggestion or hints on how I can tackle this.

PS: I had a local installation of Magento community version and it worked perfectly fine.

I checked this link already : Magento Place Order on Checkout redirects back to cart

Edit: 15-Nov-2015

Here are the contents of the log file:

2015-11-13T07:18:03+00:00 ERR (3): 
exception 'Zend_Mail_Transport_Exception' with message 'Unable to send mail. ' in /home/whymrvca/public_html/magento/lib/Zend/Mail/Transport/Sendmail.php:137
Stack trace:
#0 /home/whymrvca/public_html/magento/lib/Zend/Mail/Transport/Abstract.php(348): Zend_Mail_Transport_Sendmail->_sendMail()
#1 /home/whymrvca/public_html/magento/lib/Zend/Mail.php(1194): Zend_Mail_Transport_Abstract->send(Object(Zend_Mail))
#2 /home/whymrvca/public_html/magento/app/code/core/Mage/Core/Model/Email/Queue.php(236): Zend_Mail->send()
#3 [internal function]: Mage_Core_Model_Email_Queue->send(Object(Mage_Cron_Model_Schedule))
#4 /home/whymrvca/public_html/magento/app/code/core/Mage/Cron/Model/Observer.php(326): call_user_func_array(Array, Array)
#5 /home/whymrvca/public_html/magento/app/code/core/Mage/Cron/Model/Observer.php(72): Mage_Cron_Model_Observer->_processJob(Object(Mage_Cron_Model_Schedule), Object(Mage_Core_Model_Config_Element))
#6 /home/whymrvca/public_html/magento/app/code/core/Mage/Core/Model/App.php(1357): Mage_Cron_Model_Observer->dispatch(Object(Varien_Event_Observer))
#7 /home/whymrvca/public_html/magento/app/code/core/Mage/Core/Model/App.php(1336): Mage_Core_Model_App->_callObserverMethod(Object(Mage_Cron_Model_Observer), 'dispatch', Object(Varien_Event_Observer))
#8 /home/whymrvca/public_html/magento/app/Mage.php(448): Mage_Core_Model_App->dispatchEvent('default', Array)
#9 /home/whymrvca/public_html/magento/cron.php(77): Mage::dispatchEvent('default')
#10 {main}

I have searched for this exact error, none of the solutions worked for me. I even tried disabling the SMTP send email settings in Magento backend, but it did not help.

SMTP settings are as below :

Host : localhost
port : 25