How do you say when something must be done, against any trouble?

Question

How do you say when someone needs to do something against any trouble? It doesn't care if you feel tired, or your computer is slow, or the weather is cold, or it was done with high/low quality. It must be done.

For example:

- I saw you working yesterday, late at night. Did you finish the reports? 
- Yes. My computer was slow and I was so tired, but I did it _______. I finished
  this morning.

Other example:

- Could you repair the computer?
- Yes. I did it ______. I used an old video card, but I could do it.

Answer 1

Another possibility is the word regardless:

Without paying attention to the present situation; despite the prevailing circumstances

With this word, you have a bit more flexibility with where you place it. In the second example, you could either say this:

Yes, I could do it regardless of the fact that I used an old video card.

or you could say this:

Yes, I did it. I used an old video card, but I could do it regardless.

As an aside, with this specific example, you might want to replace "could" with "was/were able to," since the word "could" can informally be used as a present-tense conditional (as an alternative to 'can'). Example:

Could you help me out with these messages?

doesn't usually mean "Were you able to help me out...?" but instead usually means "Are you able to help me out...?" This might be grammatically incorrect according to some, but it's become such a common way to use the word that it doesn't really matter anymore what the rules are with it.

Answer 2

In the first example, nonetheless is a good fit:

in spite of what has just been said

For the second example, not so much - it must come after the words indicating the trouble. It would work like this:

Yes, I used an old video card, but I could do it nonetheless.