You are not eligible for EIC if your unearned income is more than $3600. An IRA conversion is unearned income.
Also, if you have zero earned income, you also will not receive any EIC. EIC is paid on a sliding scale where if you have no earned income you don't get any (because it is a credit for earned income only), then as your income increases you get some EIC, then as your income continues to increase you get less until it phases out (because you need it less).
Basically, think of EIC as a partial rebate for social security tax for low income workers, because social security is a regressive tax (charged the same on high and low income workers). If you don't have social security-taxable income (earned income), you don't get EIC.
