Let's assume that there is nothing inside chips and we have no connectivity. I've used PDA without connectivity for 10 years and it's not a problem if data is managed wisely.
Russian Enigma-like ciphering machine - Fialka - had a device inside power supply unit which turned set of high-power resistors on to couple power changes with internal relays. It was definitely made to bypass attacks based on analysis of power consumption. Every student of electronics can think about peaks analysis, but it was late 1950s, oscillograph was the most sophisticated device they had.
Few months ago I found a document, probably on Priyom or large Simon Mason's Number Stations site (currently in quite big neglect), which was a set of instructions for covert agents from 1960s maybe. To sum up, radio receiver tuned to some frequency can be located by locating its internal middle-frequency generator and it can be located by power interferences it introduces. There is a shielding mechanism for computer, it is called TEMPEST.
I've personally seen something like a TEMPEST-ready server, Pentium-II class machine used to process data which well.. definitely should not leak. I could even buy it from junk without drives, BIOS and RAM, yet I had no manpower to move it to my house... and my attic would definitely collapse then. Everything covered with metal plates, 0.5-1mm thick. CD and floppy disk drives in a metal container accessible with metal doors on hinges. On all sides of doors, rotatable U-shaped "locks" filled with some elastic, conductive thing contacting doors for better grounding. Power fed through built-in UPS. Most I/O ports connected through small, sealed coil units (no idea what are they for). And... NO VGA. VGA connector was literally desoldered from graphics card PCB (like BNC from network adapter), only composite output survived and it seems that it has been used.
So assuming there is nothing in chips, it would be needed to shield everything with quite large amount of metal to prevent RF going in and out. I read a blog (in Polish, who knows Virut botnet, knows who I'm talking about) written by a man who is a bit more paranoid about data leaks than average user
, and he experimented with shielding displays using glass panels with some chemicals inside.
To check the chips, it would be needed to perform etching and coloring (authors from e.g. ZeptoBars blog do it to share shots of different chips dies) and reverse-analyse it against documentation.
So if both low-level layers: RF and silicon, are checked, silicon can be audited against backdoors (RAM flipping, etc.) and then research can go slowly towards software.
Anyone knows a computer which has such audits realized in 10%? OK, not counting 74-based CPUs.