1) dont use DOS or Win95. Actually, some machines can hibernate in DOS as the functionality is built into the hardware (many laptops, for instance). Of course, boot time into DOS isn't really the issue here. DOS can boot off of HDD faster than the average arcade monitor can warm up. I'd actually think linux would be the perfect OS for an arcade machine, if not out of many folks ability to configure. Maybe it's time for an arcade distro..
2) WTF would you need 4 gigs of memory in an arcade cabinet for? You wouldn't have a good reason for this much RAM in any gaming rig. Don't let the "x-treme PC" posers fool you. Even so, 4 gigs from a good fast SATA drive would probably still be faster than a warm reboot of a full-out XP Pro install.
3) So reboot once in a while. This isn't much of a problem in XP, but it can happen if the application software is poorly designed/written. I rarely reboot the PC in my office, and when I have to, it's because something I've coded borked it all up. Still, it's yet another good reason for a dedicated linux arcade distro, though.
At any rate, a solid-state drive, RAM or otherwise, won't significantly increase your boot time. Sure the actual load times will be quicker, but most of the time you're waiting is for services to start, hardware to be initialized, waiting for DHCP negotiation on the network, auto-discovery and all that stuff.
If you trim out all unneeded services (a standalone mame box should need, well, virtually none of them) boot time should be no problem.
IIRC, you can nix the password thing by killing the windows logon client service.