No you can't add closing costs to the purchase loan. If you don't have the cash to pay for closing costs, you can try to negotiate it with the seller. It's the seller's decision. They don't have to pay for it if they don't want to or they can split it with you.
The big issue is appraisal. You will be required to pay for an appraisal by your lender because your lender needs an independent 3rd party to give a value for the home you are buying. Your lender will give you a loan UP TO the appraised value of the home - not $1.00 over.
The numbers you gave in your question is confusing. Typically closing costs = 1 - 2% of the purchase price. Therefore on a $70,000. Loan, the closing costs = $700. - $1,400. not $4,000.
You need to save money to pay for your own closing costs