Can it be that a blood test suspect heart problems?

Yes. But, misses too: Blood test can show if you have currently active heart attack (troponin) and if you have had very recent heart attack (cpk/mb). Also, cardiac CRP can suggest risk of heart disease. High cholesterol can suggest risk of heart disease but many have it with normal heart. Blood tests can be ok still with heart problems. If doc suspects heart problem he will add ekg and echo (ultrasound) to blood work.