Upgrade from 1.51 to 1.54, Admin Works OK but store does NOT

[SignaGen2]

Shopping cart upgraded from 1.51 to 1.54, today dedicated SSL bought and installed. Set Enable SSL to be "true" for the two configure.php. Tested https://xxxx.com and it worked.

Then an attempt to check out is performed and it turned out that Admin Works OK but store does NOT work for checkout.

The symptom is:
Login to Admin Ok via Firefox with URL bar status showing https://xxxx.com/admin/index.php
For storefront, click My Account and able to login only with http://xxxx.com/index.php?main_page=login rather than https://xxxx.com/index.php?main_page=login. For previous version 1.51, whenever click My Account, the URL stats will automatically tun to "https://xxxx.com/..."

Then try to check out without https://xxxx.com/......, PayPal payment module fails to show up though PayPal is configured well and turned on.

The even odd thing is from Admin>Who's Online, the URL during checkout is always like /ajax.php?act=ajaxPayment&method=setNoscriptCookie

Any suggestion?