Apparently the (extremely simple) solution to this problem was setting the Base Currency to US Dollars. The website I worked on was for the Chinese market and as such had the Chinese Yuan as Base Currency instead. Changing this to USD made the PayPal button appear instantly...

1. First of all, please check whether the module "Mage_Paypal" is enabled or not, in System > Configuration > Advanced, for the "Default Config" Configuration Scope. If it is not yet enabled, then you should enable it, to make use of this Payment Gateway. If you have changed anything, you should save that page.
2. Now go to System > Configuration > Payment Methods, for the same Configuration Scope. There are many Payment Methods listed, but most of them are not enabled. So you should select which PayPal method you want, & then make it enabled. Edit all the features of that Payment module, whichever you want, and then save it.
3. Now again clear the cache management fully & see the checkout page. The enabled PayPal module should crop up now.

There is no need to change the code because it just happens due to Paypal. Paypal does not support all the currency all over the world. Paypal supports only few of the currencies like US dollar Euro and other list you will get on website of Paypal. So what you have to check is, just go to Admin panel -> system-> Configuration-> currency setup and check your base currency . If that currency is supported by Paypal then paypal is visible on Checkout page otherwise it will not be visible.

P.S : Please don t forget to enable Paypal first.

I just need to answer this in detail:

Create the file Config.php in: /app/code/local/Mage/Paypal/Model/Config.php

Step 1 Copy the file from

/app/code/core/Mage/Paypal/Model/Config.php

to

/app/code/local/Mage/Paypal/Model/Config.php

Step 2

Look for the: $_supportedCurrencyCodes -> line 207

Then add your currency to:

protected $_supportedCurrencyCodes = array( AUD , CAD , CZK , DKK , EUR , HKD , HUF , ILS , JPY , MXN , NOK , NZD , PLN , GBP , SGD , SEK , CHF , USD , TWD , THB );

Our currency (PHP) which was not supported so I added it on the code. It should become like this:

protected $_supportedCurrencyCodes = array( AUD , CAD , CZK , DKK , EUR , HKD , HUF , ILS , JPY , MXN , NOK , NZD , PLN , GBP , SGD , SEK , CHF , USD , TWD , THB , PHP );

Then make that as your base currency (instead of USD). Hope this helps