The hardware may have some fault that could be the cause of the flickering screen.
So that may be something to watch out for. There may be Console utility logs from
the exact time of day (hour/min/sec) with details about that situation.
You may try resetting the computer using SMC reset instructions; the part of this which
may help involves power reset... Also, a different reset NVRAM may have another effect
and these will not cause harm. This could be considered part of troubleshooting, as it
does not offer a cure to failing display components or other hardware wearing out.
• Resetting the System Management Controller (SMC) on your Mac - Apple Support
read through this support document before trying anything.
• How to Reset NVRAM on your Mac - Apple Support
Some users let computer chime three times, on reset, using this. Be sure audio is not muted.
Given the age of the computer, there may be an inverter or other display part that could be
wearing out. There are a few parts that could cause that symptom; and if the flicker may
occur when moving (open/close) the display, there is a circuit from the logic board to display
that may have to be replaced with a new cable or other part. And if the computer is still using
the original hard disk drive, that to is a moving part (rotational with styli) & could be replaced.
• How to Download and Install Firefox on Mac - Mozilla Firefox Help:
https://support.mozilla.org/en-US/kb/how-download-and-install-firefox-mac
The browser. You should have no trouble using Firefox since they have a recent build for use
in Snow Leopard 10.6.8. It is probably the only updated browser for older Intel-based Mac now.
A repair to the computer may involve the display inverter or other components, best to contact
an authorized Apple service provider who will work on older vintage MacBook models and who
can get the parts. The Apple Store won't repair vintage computers, reputable options exist.
Or you could read-up on some of the more common issues & answers to see if your skills may
be adequate to attempt a DIY repair. (Or use the guide to see what it may entail to repair?)
Although an Apple Store genius appointment may be helpful if they could test or inspect the unit
unless it exhibits odd behavior during a visit, they may not be able to offer suggestions; usually
an official Apple Store's Genius visit has little or no cost for advice. Older computer issues are
usually outside of their current Applecare, parts, and warranty stream. And with some models,
product knowledge is best found at an authorized Apple specialist or reputable service location.
They would be more likely to have sources of parts and knowledge of how to fix older models.
• MacBook Core 2 Duo repair guides - iFixit.com:
https://www.ifixit.com/Device/MacBook_Core_2_Duo
There are repair guides online, such as those at the iFixit.com site for Mac repairs and these do
give you a good look inside the computer & parts are shown along with sequences to takeapart.
Sources for parts and service include companies who accept portable computers when shipped
to their repair facilities; these may vary and are across the country. (Or in several countries.)
Two I've read about in the US, are not exclusive but serve as examples: wegenermedia.com
and powerbookmedic.com -- I've sent a portable Apple computer to wegenermedia from Alaska
on the basis of good reputation some years ago; they did a good enough job that when I got the
portable back (it was in great condition, with original box, and software) I finally resold it to an
older guy 30 miles away who had never owned a computer before. He was 85 y/o & used it 5 yrs.
I provided two years support (as a neighbor in a small underpopulated area) & helped him learn.
And did not charge for helping him figure out the internet, wireless, printing, and so on.
So the computer you have may be worth the cost to check it over, or you could get another nearly
like that, already repaired, for what some businesses may charge to fix that one. I have a MacBook
(MB1.1 1.83GHz 13-inch) with 2GB RAM, 160GB HDD, OS X 10.5.8; and it flickers occasionally.
The unit works best if opened and set in place as a desktop unit with USB keyboard & mouse so
the display does not move much. So that flickers much less in that situation. You mileage may vary.
Good luck & happy computing!