Hello, my name is***** and I have over 20 years of experience as veterinarian.
I'm sorry to hear that your fellow has been limping on his front leg. I suspect he is more painful jumping down because he must catch himself and bear weight on that sore leg, or risk a fall/collapse, when jumping down but when jumping up he can transfer most of his weight to his other legs, so it is less painful.
Does his limp worsen with exercise?
Is there any swelling on any of the joints of his affected leg?
I know that he doesn't seem painful with touching his leg but is there any pain when you try to flex or extend any of the joints in that leg?
Is he bigger then normal for his breed or overweight?
What are you feeding him?
Since he doesn't seem to react too much to palpation and given your history it is likely that this is a soft tissue (ligament or tendon) or cartilage problem with one of his joints, or that he hurt his neck and the nerve roots to that leg were affected.
If he is a large breed middle aged to older dog we can see bone tumors that cause nonspecific pain, but usually your veterinarian can find an area of firm swelling and discomfort with careful palpation. Try to look at him and evaluate his sore front leg conformation compared to his other one. Look for areas of swelling or muscle loss.
Common problems in larger breed dogs are elbow dysplasia, or shoulder OCD (osteochondrosis dessicans) and secondary arthritis from those conditions. These all worsen with exercise or excess use. They are diagnosed by radiographs most of the time but sometimes require an MRI to diagnose.
Bicipital tendon injuries are possible, but we usually see those in dogs that are working dogs or in agility as these tend to be due to chronic over-use and stress on the tendon.
Because his limp is severe enough that he still doesn't want to bear weight this morning I highly recommend that he see his veterinarian. They will examine him to look for the painful area and will likely want to take radiographs under sedation. Treatment will depend upon diagnosis but can include rest and anti-inflammatories, physical therapy, and omega 3 fatty acids and glucosamine chondroitin supplements to possible surgery to remove cartilage flaps depending upon the problem.
In the meantime I do recommend strict rest. Soft tissue injuries can take months of rest to heal and won't heal if he continues to return to full activity too soon.
If this is related to arthritis I also recommend glucosamine/chondroitin products (like cosequin-ds) plus omega-3 fatty acids. Adding an omega 3 which is a natural anti-inflammatory will help as together they work synergistically, better than either one alone. These supplements can take 6 to 8 weeks to see an improvement with their use.
Best of luck with your fellow, please let me know if you have any further questions.