Most likely, however it is difficult to render any meaningful advice, without first examining your source code and a schematic of the design.
If all you have is a HEX file, with no accompanying source code, the reasons for the issues you face are numerous, as you've relied on the judgement and skills of the person whom originally compiled the code.
Some possible sources of the issue are improperly set configuration bits for your particular implementation or perhaps the HEX file does not include any configuration bit settings.
The original source code may have been written for a particular system clock frequency or a particular source of the system clock.
Also, you should be aware the actual process of programming a PIC microcontroller does not require a oscillator/system clock to be implemented, as the clock source originates from the programmer device. Even though you may have verified that the contents of the HEX have been successfully downloaded into the microcontroller, it does not guarantee it will function as expected.
Therefore to assist you further, you will need to elaborate on the specifics of your design, its purpose, which PIC microcontroller you are utilizing, posting or uploading a detailed schematic of the design and the source code. Barring that and the source code is not available, then uploading the HEX may provide some insight in the source of the issues.
BigDog