Hi.
My guess would be that it's simply the lid of the laptop blocking the GPS antenna. The antenna is probably either in the lid somewhere around the sides of the LCD, or knowing the common dimensions of a GPS patch antenna, more likely under the laptop keyboard surround. The metal EMC shielding in the lid, never mind the LCD panel itself, will be more than enough to completely block the GPS signals, which are extremely weak compared to either cellular signals or WiFi.
If you can get the thing to output the $GPGGA sentence, look at the sixth field and it will immediately tell you whether this is the problem. It is most likely giving 0 in this field, indicating no fix. It should be 1 (GPS) or 2 (DGPS) when the fix is valid. You could also test this by finding the mechanism which detects the closure status of the lid and overriding it so the machine thinks the lid is closed when it isn't. There is usually a small switch somewhere, either on the hinges or in the latch mechanism. A toothpick should suffice as a debugging tool.
If the lid closure is triggering a shutdown in some way, defeating the switch should provoke it with the lid open. If it still works, there's your problem.
This is a good reference for NMEA sentences. I've done quite a lot of work with GPS systems over the years, and parsing the data is pretty easy. But actually receiving a signal can sometimes be an issue

Modern chipsets are absurdly sensitive, but there are limits.
pca