Can I take new (still in their boxes) PC parts in my checked in luggage?

I would not anticipate any problems with security upon departing the UK. People travel with those sorts of items all the time, and none of them are listed as prohibited by the UK Civil Aviation Authority, as far as I can tell

When you arrive in South Africa, you will need to declare these goods by going through the red channel, as their value exceeds ZAR 5000 (about £270). See https://www.sars.gov.za/ClientSegments/Customs-Excise/Travellers/Pages/Arrival-in-SA.aspx. At the very least, it seems you will have to pay VAT of 15%, and possibly additional duties besides. There is an option to pay a flat rate of 20% on goods valued up to ZAR 20000, but it seems you are over that as well. So you should budget several hundred pounds for this. Having the receipts may help prove the value of the items in case customs thinks they are worth more.

In the UK security knows what computer parts are and how they look on the screens. If in doubt they might ask you to unpack an item so they can actually see it.

You should bring these items in your hand luggage, as valuables and breakables should not be packed in your hold luggage. But you seem to have too much for your hand luggage. In that case you will have to pack some in your hold luggage and take the risk it goes missing or gets broken.

The UK side will only check whether you can do damage to the plane and the people in it and most computer parts are not known to be dangerous. Batteries should not go into hold luggage.

When you arrive at the other end you will have to declare, the customs in South Africa will value and charge you to what they think it is worth. It does not matter whether you still have the parts in boxes or home wrapped as they will judge by eye whether they are new or almost new and charge accordingly.

Never lie to immigration and customs officers, as they can make your life hard if you do, and trying to hide the fact that they are new is a kind of lying. Some people will be able to pull it off, the rest will be charged for new parts with possibly an extra charge for trying to deceive.
As you will get your hold luggage before you go through customs, it does not matter in which part of your luggage you have your computer parts.

With a value of 2000 pound, I am pretty sure customs in South Africa will want to charge you.
Only if you or your husband will bring them out soon, you might get away with a 'temporary import' although I am not sure how they handle that in South Africa.

Check if you fulfill the conditions stated here:

Tax on shopping and services

Tax-free shopping
You can sometimes get VAT refunds on goods bought in the UK if you:

• visit the UK but live outside the EU and are going back home
• are an EU resident leaving the EU for 12 months or more
• are a non-EU resident but work or study in the UK and are leaving the EU for 12 months or more

Not all retailers offer tax-free shopping and you can only get VAT refunds for goods bought within the last 3 months.

Then at least tax would only have to be paid once.
If you do fullfil the conditions, the site contains information on how this is to be done.

These general rules apply for all Non-EU residents in the EU

• when exporting goods bought in the EU

After Brexit, these will probably still apply

• Products bought in UK by Non-British residents
• Products bought in EU by Non-EU residents
  • VAT would have to be refunded inside the Market it was bought in
  • VAT would have to be paid to the Market being imported to

Market = Customs Area