Several things can cause the problem you are describing, I will list some of the more common and try my best to explain each.
On a 96 444E there is what is called a turbo back pressure device. What this is is a flapper in the exhaust outlet of the turbo charger. Its function is to help the engine reach normal operating temp faster by blocking the exhaust. This will open up once the oil temp reaches 140 degrees. When closed it will reduce engine power except for full throttle. Yours may be malfunctioning and staying closed when it should be open.
Next would be oil quality. The injectors in your engine are hydraulic actuated, the hydraulic force comes from the engine oil via the high pressure oil pump. If your oil is in need of a change or the wrong API spec your injectors will not fire properly. You need to run a good quality 15w-40 diesel engine oil meeting spec cf-4 or higher, I believe they are up to cj-4 currently. If your engine is high miles and seems hard starting you may also have injector orings leaking, this would require a shop to test for and repair.
After all is said and done there are some sensors and one regulator that directly affect performance. First would be the IPR sensor, (injection pressure), it is located on one of your cylinder heads near the front it senses the oil pressure supplied to the injectors. The pressure is regulated by the IPR valve located on the left side of the high pressure oil pump in the front of the lifter valley, really hard to see but check the wires going to it. Next is the exhaust back pressure sensor sensor it tells the computer what the exhaust back pressure device is doing. And a boost sensor that tells the computer how much boost the turbo is making.
If you are getting a check engine light it may be best to get some flash codes out of it before digging much deeper. To get the codes hold down the diagnostic button on the dash and turn the key on, release the button and count the flash codes on the engine light, they are three digit codes. Post back with them.