In a case like this, the practical difference between the two words is social, not a matter of definition.
I've never heard of "can" holding more authority than "could"; certainly never seen any official definition stating this to be true.
They are both slang terms replacing another word. They mean the same thing and every native English speaker will understand that upon hearing the sentence, though the person may prefer one over the other.
Both words fill in for a few other words. The definition of "can" changes depending on which word it is replacing.
"Can" filling in for "may":
- Sitting at the computer can hurt your eyes. / Sitting at the computer may hurt your eyes.
"Could" is used to replace "may" as well.
- Sitting at the computer could hurt your eyes. / Sitting at the computer may hurt your eyes.
"Can"/"Could" filling in for "will":
- I can/could do that. / I will do that.
- Can/could you help / Will you help?
Unless you're speaking / writing formally, it's unlikely that which word you use really matters, though as others have mentioned, you're more likely to be told "yes" to your question when you use the word which the other person prefers.
When in doubt, I stay away from slang. I might sound a little snobby, but it provides for clearer communication and avoids confusion like this. You can even turn to science if you don't want the personal responsibility of being accurate:
"Studies have shown that spending too much time at the computer leads to eye disorders."
Hope this helps clear things up! :)