A myocardial infarction may contribute to heart failure due to the death of viable cardiac muscle cells. Fewer muscle cells means a reduced ability for the heart to do its job: pumping blood!
Untreated hypertension can lead to atherosclerosis, and increased resistance. This means the heart must work harder on each beat to overcome the resistance to pump blood into the circulation. Over time, the heart will wear out.
A stroke does not affect the hearts ability to pump, and diabetes has no direct link to causing heart failure.
As a side note, the thiazolidinediones (TZDs), pioglitazone and rosiglitazone, are used to treat diabetes and have been shown to worsen and cause new onset heart failure by increasing fluid retention, and should be avoided in patients with advanced (Stage III or IV) heart failure.