1) Regarding targeting, you should learn about geo-targeting options available. Just as I can set my ad distribution only to show for US/English only searches (or any other setting) there are a mirage of ways to set your distribution based on the specific geographic region you want to target. This includes setting a location and radius.. so there is the flexibility to distribute your ads only to within the geographic region you want to target. In this scenario, you might target "computer support" as a broad term but only distributed to users from your targeted geographic location.
Other options also include language, worldwide, country, state, city, dma region, zip, etc.
This is set within your account settings and determines the distribution of your ads to users based on their geographic location. So it can be done and can work based on my experiences. A generic scenario might be a new york city restuarant with the keyword "restaurant" but only distributed to a 20 mile radius from their physical location. Realize this is only one example of local search marketing, there are many more ... and you should become more familiar with how to get listed in yellow page listings and other local listings. For example, Google does provide a free local listing service - see here
as well. I'm not sure if that is only US.
2) Regarding your second concern, about people not searching on Internet because their computer is broken thus needing service... that seems logical but you never really know until you try/test. First many/most have access to more than one computer (library, friend, work, etc). Second, their service needed may not be for themselves. I don't know, you may be right but based on my experiences you have to test. Additionally, it is a consideration when it comes to evaluating other marketing. how else do you need to get out their locally? Is presentations/lessons at chamber sponsored events? yellow pages? advertising in local paper/radio/tv? the best is to find more than one tactic that works for any marketing. In yours, adwords may be effective but other tactics should also be researched/tested.
Based on my experiences when targeting local, it is often best if not an either/or thing ... for example - list in yellow pages referencing web site. They see ad, check you out on web ... then call.
Because your audience is limited, the numbers of people looking for your services is more limited - so more than point should be considered imo. The benefit is that when your ad is clicked on, they are a highly qualified lead that matches the business you are targeting.
Really, it doesn't cost much to test as if no one searches based on your distribution there isn't a cost as the only cost is based on pay per click. If they do meet your qualifications, then you find out and they'll be qualified and hopefully worth the associated costs. If you set a budget, you can test this without much risk to evaluate the viability.