When a .com is gone, you can usually find a variation.
Without looking first:
allcomputerwork.com is gone, try allcomputersfixed.com, computerrepairs.com, allcomputer'Z'.com etc. For example, Snake Eyes, one of my fav up and coming bands in London tried to get snakeeyes.com (the movie got that one of course) so instead of using a .net, .org etc. they registered snakeeyesmusic.com
Now as a rule, URL's should be short, but with the amount of URL's used and lack of domains available, they are getting MUCH longer as time passes and people are not trying to remember http or www anymore, longer URL's as unfavorable as they are have now become commonplace. Another way is to use acronyms. ComputerAssociates.com is now CAI.com etc.
You're right though Jules, your company name and 'appearance' is the big thing. You could be a one man operation and appear to be a corporation. Then again, I've seen corporations appear to be one man operations and not even offer a support phone number online, yet they are a VERY large company!
The internet hides and masks the truth, those who can take advantage of the larger than life appearance they can achieve online will generally succeed faster than those that don't.
I have made small (yet very talented) garage bands APPEAR to be Canada's leading artists, they get gobbled up in Europe. you don't have to lie, you don't have to deceive, with the internet ANYONE can be larger than life. I am a self employed yet far from wealthy independant IT consultant, commmunications consultant (and several other 'consultants'), I manage several relatively successful bands, but I am no Bruce Alan by any means, yet within the industry, I am treated as if I am.
Who you appear to be will help you become who you WANT to be.