Is it possible that feeling tired all the time have anything to do with a blocked artery?

Blocked where?: Vascular disease per se causes ischemia, low-flow to whatever its perfusing. If you have hyperlipidemia, hypertension, diabetes and smoke, these all collude together to occlude arteries, everywhere--it's only a matter of degrees. Yet global fatigue per se is not diagnostic of vascular disease. Clinical depression causes fatigue and burn-out without effecting the vascular tree.