What your going to have to do is download whatever driver they have, i.e. XP or Vista driver and then install it via the control panel (add new hardware). It may not install all the way, which in case it doesn't, ensure that it has sat for awhile and then restart the computer. That should get you up and scanning.
Looking for a driver, HP doesn't have offer driver for a scan jet 4400C running under Win 7 - 64bit.
I solved this problem by installing my XP original CD on a virtual machine created on my system (Win7 Home Premium 32bits) using "VMWare Player" - a free program.
After the virtual machine was created, I installed the scanner drivers using the original HP Scanjet 4400C disc.
Now I have not only my scanner running, but some old programs and games running as well.