Can I have problem when applying for GC because I didn't go to school after been aproved for F-1 visa

You need to consult with an immigration attorney. It is not possible to tell from your question when you fell out of status, or whether you are now unlawfully present - there may be very serious consequences if you never attended the school for which you were granted F-1 status. Although J-1 and F-1 nonimmigrants are admitted for "duration of status" (D/S) and do not automatically start to accrue unlawful presence as of the end date of an approved academic program shown on the underlying Form DS-2019 or I-20, individual scholars and students in these statuses can begin to accrue unlawful presence if they fail to register for school, fail to show up for classes or maintain a full courseload, or drop out of school altogether, as the designated foreign student officer must annotate these events in the SEVIS database, which is monitored by ICE and USCIS. However, even as a former student who has failed to maintain valid status for the past 4 years, that alone would not prevent you from obtaining residence based on marriage to a US citizen: the real question you have raised here is whether you are eligible to adjust status to permanent resident at all, because you previously held J-1 status. If your J-1 program required you to return to your home country for two years, then even marrying a US citizen will not overcome that requirement. Therefore, you need to find any documents you have relating to your past J-1 and F-1 status and meet with a qualified immigration attorney, to find out whether you are subject to the 2-year foreign residence requirement (INA 212e), and whether you may have any grounds on which to apply for a waiver of that requirement.

This is general information only; it is not intended as a substitute for legal advice, and does not create an attorney-client relationship.