Health Care Relief Act of 2004 - Amends the Internal Revenue Code to allow: (1) taxpayers, including non-itemizing taxpayers, a tax deduction from gross income for the first $2,000 of their out-of-pocket medical expenses; (2) certain small business employers a business tax credit for amounts paid for employee health insurance coverage; and (3) a refundable tax credit up to $500 for the health insurance costs of a taxpayer and the taxpayer's spouse and dependents.