I turn on my system and it works ok for a couple of minutes. Then it started showing "fan check" for another minute, then shuts itself down. Is it the fan? How can I check that?

To answer your question, yes, it is the fan. There will be screws holding the top cover onto the unit; remove these, and find the fan(also remove any dust you find inside, as this also could render the fan useless due to airflow problems). Make sure it's not jammed or clogged or anything such, and plug the unit in, turn it on, and make sure the fan turns on(in some cases, it waits a maximum of one minute to do so.) If it does not turn on after one minute, then a new fan is needed. Any fan with the same size and power connector will do.