Ok, I don't normally post, but I have to set the record straight. You do NOT have to rig the game to beat civ3 conquests at Sid. However, you must understand quite a lot about the game, and you must micromanage everything, and even then you may need a little luck. That is, I don't think anyone can win every single random game at Sid level.
I've been playing Civ since the DOS days, and often. Now my favorite game is Sid level, huge map, 15 opposing AI, raging hordes, and EVERYTHING else random (normal aggressiveness). This setting is suicide for a newbie, but I assure you that I win more often than I lose (maybe closer to even if you count the games I abort very early because my starting position is badly damaged by barbs or evil neighbors almost right away).
Sometimes you take risks that don't pay off and if things go too badly you get the sense of when to throw in the towel. But you'd be surprised how small and pathetic you can be in relation to all the AI and still end up winning.
First advice is practice every civ and really learn how to exploit strengths and weaknesses. Use diplomacy often and get comfortable checking most known civs for possible deals every turn (you'll need it at the high levels).
Start playing whatever level lets you win sometimes but lose often. Then figure out how to change that to win often, lose rarely. Then move up.
The key is that the game itself changes as you move up. That's part of the fun. At low levels you can do anything you want, but if you want to move up you need to learn how to adjust your strategy according to your civ advantages, your terrain, your nearby civs, your borders, what you can buy/sell/trade etc.
At Sid it is impossible to keep up with the AI early, so you must learn a skill not needed at lower levels: how to play "catch up". You must placate all opponents early, usually, and most opponents nearly all game, because you definitely can't fight more than one AI, and usually even then you can only fight effectively in "Blitzes". Use much diplomacy to keep most civs polite to gracious (easier said than done), and let no one be furious for long unless you want war.
Then, buy/sell/trade to acquire resources, luxuries, and techs (the AI will get them first nearly all game until you catch up, if you ever do). Form alliances. Since Ai builds at twice your rate, you have no hope to beat it one on one in a long war. But if you have 14 allies you may wipe up an otherwise unbeatable opponent. Plus you'll make lots of AI "friends" who will give you good terms on your deals.
It follows that you should avoid MPP unless you're very weak and suspect you can't get allies otherwise. Usually an MPP will only draw you into a war you can't win sooner or later, and you'll have to pay big to get out of it, and risk breaking an alliance in the process.
ROP is a real friend, though, provided that the AI on the other end isn't likely to sneak attack, or provided that you might welcome the typically lame sneak attack that might come initially so that you could fight a war without any damage to your relations with other AI.
Finally, when you first start playing a level, abort bad starts. The reason is not just that you're less likely to win. The reason is that you may not get to finish the game. Then you don't get to practice the whole game, so you don't get better as quickly. Alternatively, you could "tailor" your civ to a particular map to insure a good start. For instance, seafaring civ on an island map, etc. The danger of that is you will fall in love with a particular civ and not learn how to play the others.
One more comment about Sid. All the stuff they tell you in the forum about strategies for city placement, etc. goes out the window. Oh, you need to know it all, just in case you can use it. However, the reality is you get your cities in anywhere you can, because the AI will crowd you so quickly as to make you want to scream. And the AI will cheat. That is, it will grab all of those resources that you can't see. So you just grab as much and as good land as you can as fast as you can. Then you hope to be able to defend it and populate it more densely. Then military buidup (usually) and attack for new scraps of land one bit at a time.
My last game (finished this weekend) was set as I described above, and I got Aztecs on a barren, icy rock (many mountains) in the North Sea. Not a good start. Worse, not a single luxury on the rock. But enough land for about 20 very crowded (close together) cities. Of course, another civ invaded my rock before I could settle it all, so I prepared for war, etc. Anyway, I eventually got the whole rock and built it up. I won this awful start (diplomatic victory about 1500 AD) without taking advantage of save/load, etc. So it's quite doable. But it takes lots of practice. Good luck!
ps. Reply about stealing. Yes, there are times you want to steal techs at Sid, because it's often so much cheaper than buying. But remember that this often leads to war. Hence you steal always from one or two civs all game because you can't afford more to be pissed at you. Once you get espionage you always steal from the civ you are fighting. Never steal from any civ with which you have good relations. It's not worth it, except, of course, something like fission if you think you can build UN before AI or Literacy for Gr. Lib, etc. But most of the game at Sid you can forget about wonders. They're for the AI. You won't have the tech to start them first and you can't build anywhere near as fast. The only thing I do is record (on a piece of paper) where each wonder is built because of course my miserable, ignorant hordes dream of the day when we might conquer such a wonder and claim it as our own.