I am going to the US on a work visa and would like to take my desktop computer with... am I allowed to take only the tower through customs if I pack it in a travel case?
Yes no problem at all and if you are bringing it back with you when you leave you don’t have to declare it and pay tax.
Reason being that you are always allowed to bring personal items across the border ( within reason ) without having to declare and pay tax.
If, however, the computer would stay in the country when you leave you would have to declare it and pay the tax at the border when you enter, also if the computer is new and in its original packing customs may decide that you are either bringing sales samples into the country or you brought it to sell it and then they will force you to pay the taxes on the computer regardless of what you say about it.
I have personally done both.
carried a used personal tower over without problem.
carried a new PC over, declared it and paid the taxes at the border and sold it .
Both the above are very pain free and not really a hassle at all.