If you were actively engaged in ongoing business activities with a profit motive in 2023, then you file a schedule C for 2023, even if your first customer didn't pay you until 2024. You will show a loss that can be carried forward to offset future profits. List the computer as an asset. Since it was under $2500, you have the option of depreciating it over time or taking the entire cost as an expense. You are correct that if it will only be used 80% for business, you only deduct or depreciate 80% of the cost. In addition, if you expense or depreciate 80% of the cost, your new adjusted cost basis is about $200. This is important because, if you sell the computer (used, trade-in, etc) at any time in the future, if the selling price is more than the adjusted cost basis, the difference is business income (because you are recovering some of that expense you previously deducted.)
If you did not start active and ongoing business activities until 2024, then you report all your business activities on your 2024 tax return, including placing this computer "in service" for the business.
