Correction: He was taken to the hospital during rush hour for a serious case of blood cancer with an irregular heartbeat.

You cannot say 'as' a serious case of Cancer you have to say with a serious case of cancer. Heartbeat is a noun so it needs a definite article plus you need an and ei. and with an irregular heartbeat.

Peter/Brittany - it's up to you of course, but you might want to put your comments in as 'answers' (rather than as 'comments') - that way the OP can select an answer they think is best - which means you receive some form of points acknowledgement from italki (which helps with things like teacher ratings) - and also the question gets moved to the resolved questions part of the site

Hello! The sentence is okay, but it would sound more natural if you said: He was taken to the hospital during rush hour WITH a serious case of blood cancer AND an irregular heartbeat. or: He was taken to the hospital during rush hour. He HAD a serious case of blood cancer with AN irregular heartbeat. or: He was taken to the hospital during rush hour BECAUSE he had a serious case of blood cancer with AN irregular heartbeat. But a native speaker would probably say: "He was taken to the hospital during rush hour because of his irregular heartbeat. He has blood cancer, so it's very serious." He probably goes to the hospital a lot for cancer treatment. THIS visit is because of his irregular heartbeat, but it's very serious because he also has cancer.

He was taken to hospital during rush hour 'due to' a serious case of blood cancer 'and an' irregular heartbeat. This flows better! I hope that helps