I don't know about CIv 3 and Civ 4, but I would guess there is not. Civ (1 I think), OTOH, has plenty of free online version (clones?), some are playing directly from browser. Including one version which implements sort of a MMO version of civ. So if you're willing to put the time and effort to get used to an old UI and very rough graphic, that might be an idea.
In the same spirit, there are
freeciv and
C-evo which have really small executables and should be playable from a USB stick (if your issue comes from restricted internet or right to install program).
Freeciv is a more or less faithfull clone of civ 2 (I played it so long ago I can't really say), including the cumbersome UI (more cumbersome actually IIRC)
C-Evo is totally awesome, with graphics only slightly better than Civ2, but a User Interface almost as intuitive as Civ 3 and much better in some aspects (mostly automation like building list, governors, etc...). The game is not a clone and has its own, very distinct and tasty flavor. It also solves most issues of civ 3 and former which are or aren't solved in civ 4 and later : production overflow, tech brokering, AI (unlike any Civ iteration, they are competitive with regular human without cheating, but somewhat lacking in diplo), automation (city governors and workers ; it explicitely does a good and controlable work, where civ 4 does a surprisingly good but confusing work under the hood), I don't remember about corruption and waste.