I started on a trap bar deadlift, the bar had the elevated handles - that helped a lot. Jim said full range was better, so I did the Anderson method - I turned the bar over to use the flush handles but put the weights on stacked rubber mats and every week or two, I would remove a mat until I got down to the floor. I was then able to eventually switch to conventional deadlift from the floor, but I practiced the movement daily with 95lbs (I have 25lb bumpers) - the whole process took about 8 months.
I had a similar issue with squats and my low back and knees, so I did hip belt squats for 4 months and then took a few months to work onto regular squats at full depth, again with daily practice and watching lots of Mark Rippetoe videos on technique - which lead to removing the low back and knee issues.
The takeaway is that the guys above are all correct IMO in that you should pursue alternative exercises that you CAN train with full range now and continue to work on your technique and mobility to eventually see if it is possible to perform standard deadlifts and squats over time. Maybe it takes a year or two to reach this point, if you can do it, but that isn't much time at all in a life long endeavor.