There are no Federal laws prohibiting a felon from running for Federal office. Local and state laws do not apply.
Section 3 of the 14th Amendment, which is aimed at anyone who “engaged in insurrection or rebellion” after taking an oath to support the Constitution could possibly apply, but it would have to be through the Congress to impose this, not through states or courts.
Yes, DJT can still run and win with a felony conviction.