I want to bring desktop components from India to USA including a processor, graphics card, motherboard, ram, ssd, and a monitor. I will be carrying it in a handheld carrying case as a check-in luggage. Will I face any problems?
You can take it on flight but there are some issues.
The main thing is damage. There may be a chance of the item to get damaged.
Also you should consider packing it in Electro-static discharge bag.
Otherwise, no issues.
Anyway you should consider the carry on regulations.
Just for a reference : http://www.latimes.com/travel/la-trb-carry-on-luggage-size-20140611-story.html