Since no one else has answered, I'll take a shot - sticking with Ancient Egypt, since that's the only area where I know anything about this subject.

Ancient Egyptians, at least those of high social status, did sometimes suffer from heart disease. An article in the Lancet ('Atherosclerosis and Diet in Ancient Egypt', Rosalie David et al) discusses this: among 16 high-status mummies where the hearts could be identified, 9 showed evidence of vascular calcification. Other examinations of affluent Egyptian mummies have found similar rates of atherosclerosis, arterial lesions, and other indicators of heart disease. One study found what may be the oldest known case of heart disease: the mummy of a princess who died in her 40s, somewhere between 1580 and 1550 BCE, had plaque build-up in her arteries.

David thinks this may have been at least partly due to diet. The mummies she was analysing were mainly priests and their family members, so she studied hieroglyphic inscriptions on temple walls, which described food offered to the gods - food which was later eaten by the priests and their families. She found that 'the diet consisted mainly of beef, wildfowl, bread, fruit, vegetables, cake, wine, and beer' - and even the bread and cake would have been heavy on saturated fats. Basically, priests and their families were eating a very fat-rich and salt-heavy diet (salt was used as a preservative), which probably goes a long way towards explaining why their arteries were in bad shape. The same may well hold for other high-status people. Lower-status people had a much more vegetarian-leaning diet, but since they were less likely to be mummified, there's less evidence available on the condition of their hearts.

So it's likely that heart attacks happened in Ancient Egypt. In fact, there's actually something that may be what you were looking for: a description of a person experiencing a heart attack. It's in the Ebers Papyrus, which was written about 1550BCE but probably based on earlier texts, and which is one of the closest things we have to an Ancient Egyptian medical textbook. It includes a list of ailments and what a healer should do about them, plus a section on how the heart and circulatory system work, and a good scattering of spells and incantations - for the Egyptians, physical and spiritual medicine worked together. Some of the things in there are still familiar to us today (honey as an antiseptic, peppermint for a stuffy nose), while others make less sense to us - the remedies have a lot more dung than you'd expect, also a lot more emphasis on the milk of a woman who has borne a son.

The Ebers scribe knew that the heart was the 'centre' of all the vessels, although he reckoned it was the source of all bodily fluids - blood, mucus, semen, urine. There are descriptions in the papyrus of the heart 'trembling', of the heart weakening as a result of old age, of 'a contraction of the chest' caused by heart disease. And there's this (quote from the Cyril Bryan translation):

When thou examinest a person with a suffering in his abdomen, he is ill in his arm, in his breast, and in the stomach-region...then thou sayest, 'It is Death that has penetrated his mouth and taken up its abode.'

That sounds a lot like a description of a heart attack.

As for what they did about it: as you say, heart surgery wasn't an option. Major surgery wasn't a great option for most of our history, due to a lack of good anaesthetics, a lack of good antiseptics (and often a lack of understanding that they were even needed), and a lack of good ways to stop the patient bleeding out. So here's what the Ebers scribe recommends for that possible heart attack:

Make him a stinging remedy from the following plants:

Tehua-berry 1

Poppy-plant 1

Peppermint 1

annek-plant 1

red-sexet-seeds 1

Cook in oil and let the patient drink.

If nothing else, the poppy would have acted as a painkiller.

There's also a remedy for sweaty feet, but you're going to need an eel from the canal.