'Sales Tax' is not displayed or calculated within cart or checkout pages.
You should set "Display prices during cart/checkout" to "Excluding tax".
I suggest you set the "Price display suffix:" to "excl Sales tax" to inform customers.
I would uncheck "Rounding" until the site is debugged.
Taking the "Triple play" item as an example, on the product page please confirm you got the regular price set to $29.99, Tax status: taxable and Tax class: standard.
I see that on the cart page, the update cart and checkout buttons don't work. Suggest you try resetting the permalinks by going to Settings / Permalinks and click Save Changes. There aren't any changes but clicking save changes should reset the permalinks.
You have version 1.3 of your theme, but the current version is 1.4 so you should update.
I'm not hopeful the above will be enough to fix everything and more work may be needed.