I agree the first one is Norfork Island Pine (NIP). It can manage to do well in surprisingly small container for the size of the tree and is pretty drought proof. Another characteristic is that it can handle semi-shade/low light indoor conditions. As such it is a very forgiving houseplant. I have NIP that was originally given to my DD as a small 1 ft desk-top Christmas tree. If I remember correctly it had been a group planting of 3 or 4, but I culled two and the remaining pair in same contsiner are maybe 4+ feet tall now.
So possible issues -- you have it in front of that large window. With winter sun, is it getting exposed to direct sunlight? This plan actually doesn't do well in hot direct sun. Mine are in a interior location and only gets direct morning sun just as it rises. Mine gets additional bright supplemental light from overhead CFL and 4-tube shop light that is about 3 feet away. (This kind of distance is considered inadequate under most circumstances). Even without supplemental light, this plant is best placed in East facing window or West facing window with limited exposure if too hot.
Temperature is another possible problem here. Do you know how cold it gets in the office during the night and over the weekend?
There is a base board heater nearby -- this may mean that the air is too dry. As a tropical, it does better with a fair amount of humidity though it is low humidity tolerant. In low humidity conditions, red spider mites can become a problem which may explain the brittle dried needles as well, though I can't tell for sure. Do you see any webbing? By the time severe infestation has taken hold, you will see network of fine webbing especially in leaf and branch nodes.
I have lots of plants that are grouped together and I mist them (every morning) to simulate morning dew. I am diligent about this in the fall when I first bring all the cold sensitive plants inside, but gradually taper off to about 3 times per week. However, this time of the year with heat running constantly, the indoor relative humidity has plummeted to unhealthy levels -- down to 30's%. I want to try to maintain 40's at least.
For the NIP, I also put the container in a larger deep tray -- this year, I'm using a caterer's tray lid -- 2 lids stacked for strength. I put water in the tray almost every day -- about 1/2 to 1 inch deep -- the water is gone and the tray dry by the time I do this again. This is supplemental to actual watering from the top, which I do probably about once or twice a week. If you only water on Monday, your trees was probably not getting enough water. When full and lush, it was probably better to water again on Friday. NOW however, the tree doesn't have enough to warrant this because you may overwater. But bottom watering as supplemental watering snd humidity aid would be a better option.
Now for the bad news -- Even though the tree is struggling to revive, the dead needle branches are probably lost. Even if they are still alive, the dried up needles will only fall and the branches will only grow new side branches of new needles, resulting in very odd appearance for this tree. I think I see two other trunks in addition to the large one. One of the them has new growth but I can't see the other.
Cleanup for these trees will be messy. You will want a plastic or canvas tarp. Put the tree container in the middle, and wearing gloves (leather or kitchen gloves) pull the branches one by one through your hand to shed the dead needles. If you want to see if they will recover, try trimming the tips -- I would start with about 1 inch -- if there is green in the cut surface, new side shoots may grow. If dried up and dead, then keep cutting to see all the way to the trunk. But if you have cut more than 1/2 of the branch, it's not worth saving because it would be too far into the interior of the tree for any new growths to grow well or grow into correct shape. Unless you can repot/uppot the trees in this location or elsewhere in the building, there is no way to do this until the weather outside is warm enough to take the pot outside. If the smaller tree(s) are dead, then just cut them at the soil level.
Once this much is done, get a tray to put under the tree's container. Seriously, caterer's trays and covers are great if you can get hold of them because they are square or round -- usually free. You CAN buy trays specifically sold for this purpose though usually ridiculously expensive for what it is. But you could get something decorative that way. Boot trays and nursery trays work but they are rectangular and you need at least 1-1/2 to 2 inch depth. You may think it would be better to put the plant container on gravel or something and use this as humidity tray -- this is a common practice and it would work. But personally, I find them difficult to use that way -- it's too easy to misjudge the amount of water to put in the tray for me, and keeping the water level below the rocks would mean the tree won't be getting actual water in supplement to regular watering. (but it might be do-able if you are dedicated -- I have too many plants....)
...in an office situation, you may be better off to write this one off as learning experience and get another one though. We have and do still all go through this, it's part of gardening and horticulture