Should I enter points paid for the entire length of the loan or only the amortized portion for the tax year and what remained since I refinanced?

Enter the balance of the points after the amortization you've taken. This intangible asset should appear on the Depreciation and Amortization Report in TurboTax. Total amortization is the sum of Prior and Current "Depr" columns.

The lender for the refinance is important. IRS Publication 936 states under Mortgage Ending Early:

“If you spread your deduction for points over the life of the mortgage, you can deduct any remaining balance in the year the mortgage ends. However, if you refinance the mortgage with the same lender, you can't deduct any remaining balance of spread points. Instead, deduct the remaining balance over the term of the new loan.  A mortgage may end early due to a prepayment, refinancing, foreclosure, or similar event.”