Past tense vs. Present Perfect tense

I was reading the book "Essential Grammar in use" Third Edition by Raymond Murphy.

In page no.56, there were some questions about using Past Tense and Present Perfect Tense. In that, one question confused me a little. I've given it below,

The washing machine was broken, but it's OK now. It __________ (repair).

My answer at first sight was "was repaired" (wrong answer) because I thought the action was completed in the past.

But the correct answer given in the book was "has been repaired". It confused me a little. However, I understood it later that the action's result "It's OK now" has been related to the present. So the answer "has been repaired" seemed correct to me.

However I always confuse this below examples,

"I sent an email to you yesterday."

"We despatched a parcel to you yesterday."

vs.

"I have sent an email to you."

"We have despatched a parcel to you."

The first one should be the most common or correct answer. But what's wrong with the second one? Can I use it? Because the mail sent / parcel despatched has some connection with the Present, because it hasn't reached them yet.

Also please clarify, whenever I use Past tense, Is it always required to tell the time of action? Eg. "I sent an email to you yesterday."

I have already asked similar questions here. But still, I have some little confusions. As a non-native English speaker, most of the time, I think that something I did in the past has some connection with the present moment and I feel like I need to use " Present Perfect".

Please help me. Thanks in advance.

Update:

This question has been marked as duplicate. The other question was also asked by me. However this one is different & more in detail than the other question. That question was about the time markers (yesterday) with Present Perfect tense. But this is about no time markers, but I'm asking that, is it OK to use Present Perfect tense when the action was happened some hours ago however the action is still connected to the present moment.

Answer

Being a non-native speaker, I too had the same confusion. However, by observing lots of examples and reading answers here, on this site, I can now be clear! I'll try to solve this for you.

It is actually the context that decides what to use when! But, please note that there are no concrete rules for what I'm saying.

Let's create a scene at some office.

There is an email regarding 'refund' from one of your clients, and this needs to be addressed immediately. You forward that mail immediately to the salesperson. You now call him and say:

I have sent you an email of Mike. Please look into the matter immediately.

Now, think that the mail had no urgency. After 4-5 hours you are meeting the salesperson and just informing/confirming about the email. You say:

I have sent you an email a couple of hours back. Did you check it?

If the matter is serious and things are ignored. In other words, there was no reply from your sales department to the client. You now emphasis that the mail is with the salesperson since quite long. Now here, quite long could be just 3 hours as well, but the delay is unpardonable. Had/have both can work. You angrily say:

I have/had sent the mail two hours ago, and still there is no reply! The client is angry.

If it is the next day, you may use had because it's now a distant past.

I had sent you an email yesterday. Please check, and go for push notification.

Again, to repeat, there is no strict rule I have come across. Depending on the situation, you use 'have/had' or neither of them. However, as I said, it will look down to me if you use 'have' and refer to the mail sent yesterday!

I have had sent you an email yesterday.

If I try to remember all the instances, I can also say that you use nothing (no had/have) while narrating the case or matter to someone. However, this could be common only in informal talk.

You know what happened yesterday? Mike, one of our clients, shot an email to me and he was completely pissed off! He wanted a refund, and the matter was pending for more than a month! I then forwarded the mail to Andrew and thankfully, all was settled.

No had/have there!