I just finished replacing a monitor on my friend's laptop because the original monitor wasn't displaying images, instead showing lots of white, lots of white lines, and nothing useful. When I just tried it now the new monitor has the same problems. there was 2 places the monitor plugged into that I saw when I fixed the monitor, is there anywhere else I need to check? or what is the easiest and safest way to troubleshoot this problem?

Plug in an external monitor. If the problem is the same on the external then something is wrong with the on-board video (ie the motherboard).

Other than that open it back up and double check the connections are in properly.

it didn't have a problem with an external monitor, so I guess I need to re-open it up. what are the odds that the cable is bad and where would I get the cable to replace the cable? (hopefully hypothetically...)

I would imagine you can also get the cable at wherever you got the display. If you got it through ebay or something then I would start my search at the manufacturers website. If it is too expensive there I would start looking for third party replacements.

The external working is a good sign the video card is fine, but it does not mean there is not something wrong with the connections on the internal side of the video components.

Hopefully it is just a matter of double checking the cables. You can also try cleaning the contacts.

If it turns out the video connection is bad you can try looking for third party motherboard refurbs. They are out there and can cost less than $100. Your friend will have to decide if it is worth it. Or you know the external works good and can use the system that way. Though that always takes the fun out of it being a laptop.

Could the video card be failing only on the internal port?

Yes it can.