What kind of tests can I take to find out whether there is a block in my heart?

A routine . ECG can usually detect a block.
Multiple. A stress test can be suggestive of a blockage. Or more invasive tests such as a cardiac catheterization or a nuclear test or even a cat scan can be diagnostic.
There are several. Resting ekg ekg with exercise or after certain medications that stress the heart. Injection of radioactive substances. The heart muscle will show up less dark in areas supplied by the blocked artery. Direct pictures of the arteries (cat scan or mri).