The CD would have been your biggest concern and since you don't have that to worry about, you can probably do it without any problems. I don't believe that it should effect the hard drive and the circuit boards will operate in any position. The only consideration other than these is will you be blocking cooling vents on the sides of the computer by lying it on its side? If so, it's probably not a good idea.
Most modern CD and hard drives can be oriented horizontally or vertically - you can check the specs to be sure.
Cooling would be a concern - since some towers are designed to draw air in through bottom vents and exhaust at the top - obviously you do not want to restrict any of the air vents. The case sides may be a problem in that they may not be designed to hold any weight.
IBM/Lenovo makes some very neat "convertible" machines which can be oriented either horizontally or vertically by simply standing them up or laying them down. If you ever get a chance, take a good look at the IBM S series - convertible - probably the best and most convenient case design out there.
When placing it on the side, make sure that you place it with the motherboard on the bottom instead of top. If you leave the cards (ie. video, sound) hanging instead of resting on top of the motherboard, you will run the risk of them getting loose over time.
Ditto about the case being able to hold the weight of the monitor. If it is a big 21" CRT, it can weigh over 80 lbs.
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