Millions of Americans will begin receiving health insurance coverage under the Affordable Care Act on Wednesday after years of contention and a rollout hobbled by delays and technical problems. The decisively new moment in the effort to overhaul the country’s health care system will test the law’s central premise: that extending coverage to far more Americans will improve the nation’s health and help many avoid crippling medical bills. Starting Wednesday, health insurance companies can no longer deny coverage to people with pre-existing conditions and cannot charge higher premiums to women than to men for the same coverage. In most cases, insurers must provide a standard set of benefits prescribed by federal law and regulations. And they cannot set dollar limits on what they spend on “essential health benefits” for a policyholder.