2005 toyota corolla engine problem?

[Izzy B]

Okay so i have been a bad car owner. I have a 2005 Toyota corolla that I have been driving for the past five and a half years and since that time I have not been changing the oil on schedule. I recently began having issues with the car since this past July. I took the car in for an oil change after about a 12 month time since the last one and there was sludge build up from the old oil. since that oil change my mechanic told me that the engine is going. I took it back to Toyota and they advised me that the engine needed to be replaced and that would cost around 3000-4000 to do that. I know i should of took better care of the car but it is what it is for now. every morning it feels like my car is about to turn off and some times when the weather is extremely cold the car cuts off on me. any exprienced mechanics out there have any good advice for me. I open to listen to everything that could help me with the mess i put myself in. the car sounds really horrible as soon as the engine starts but then after time i drive it out and it's fine.