Grammar – Difference Between ‘I Can’t Imagine…’ and ‘I Don’t Imagine…’

Won't implies either a pledge, as in your example (I promise), or a confident prediction, or a refusal:

Abduction by Martians has dropped off since the 70s. I'm pretty sure it won't happen to you again.
No matter how much you offer I won't sell you my daughter.

Can't implies either an impossibility or a directive:

I'm sorry Bobby made that rude gesture. It can't happen again, because we've cut off his hands.
Yesterday Cathy sold one customer another customer's umbrella. This can't happen again.

First, write the sentence in the positive, and see whether the verb that you want to negate is the main verb in the sentence. Consider talk in these three sentences:

he talks a lot - talk is main verb
he really likes to talk - talk is not the main verb
he likes talking - talk is not the main verb

If you want to negate the main verb and there is already an auxiliary verb (be, have, will, should could, must) in front of it, you insert not between the auxiliary and main verbs.

I am not going to the party
I have not seen him today
I will not have time tomorrow
You must not tell anybody about this

If the verb that you want to negate is be, just add not after it.

Dinner is ready
Dinner is not ready

The main verbs need and dare are special cases: in the positive, it is followed by to, and in the negative to is replaced by not.

You need to come
You need not come

For all other main verbs that don't have an auxiliary verb, you add the auxiliary verb do and then negate the auxiliary verb. The auxiliary verb has two cases: does for third person singular (he/she/it) and do for everything else. When negated, this can be written out in full do not, does not, or contracted don't, doesn't.

I want to go to the party
I don't want to go to the party

If the verb that you want to negate is not the main verb and it's preceded by to, it's an infinitive: you negate it by putting not before the to

I told him to come
I told him not to come

Likewise, if the verb you want to negate is not the main verb and it's got an '-ing' ending, then you negate it by putting not before the verb.

thinking can get you into trouble
not thinking can get you into trouble