Can a short circuit kill the USB port of a PC

There is a distinct possibility that the overload on the USB port 5V from the computer is related to the fact that you only hooked up one set of the VSS and VDD pins of the PIC16F877A. It is never safe to operate a chip in this manner as there is never any assurance that the internal MCU design even connects the various VDD pins together and the various VSS pins together with an internal low impedance connection. Lack of these external connections can cause some parts internal to the chip to not be powered correctly and result in improper forward biasing of chip junction diodes. Massive amounts of current can flow in these cases.

Also be advised if you rebuild the circuit with new parts that you also need to be adding bypass capacitors between the VSS and VDD of each chip connection.

With regard to the USB ports of your computer...It is likely that you have damaged things so bad that they may not see life again. Take this incident to re-think the process of powering experimental circuitry from your computer's USB port. Check out a place like eBay where you can find dozens of choices for very low cost USB power blocks that can supply 5V from a AC power source (or also from an automobile aux power jack) to power your experimental circuits. In the unfortunate case of a short or some oversight in the design of your circuit it is far far better to blow out a 5->10$ power brick than it is to destroy your laptop or desktop computer.

USB uses very fast signals (480 Mbits/sec at high speed) to transmit data serially. As such, it is very sensitive to transmission-line effects in the cabling. What you have done is created a "stub" connection (whichever host port isn't being used at the moment) that really messes up the data signal because of the signal reflections from both the point where the three sets of wires are joined, as well as the open end of the stub.

Bottom line is, you simply can't do that. You might be able to install a physical DPDT switch to switch between the two host connections, but even that would be questionable.