Yes, you may count the depreciation of your computer as a business expense.
In Publication
551, the IRS says
To figure the basis of property you receive as a gift, you must know its adjusted basis (defined earlier) to the donor just
before it was given to you, its FMV at the time it was given to you, and any gift tax paid on it.
You will need to figure what percent of your computer's use is business, and what percent is personal. Figure percentage based upon the time spent in each category. If you work 8 hours a day and use your computer for personal use 2 hours a day, then your business percentage is 80%.
