The computer of a character was found and searched by forensic computer experts working in law enforcement. They managed to locate just one email, which was corrupted, but still showed four or five unrelated words.
I'm going to assume that your character tried to wipe all the data from the machine, but was unsuccessful. When something is deleted, it's not typically removed -- the space it took up is simply marked as available for another file to write over when needed. If your character wants to wipe all the data properly, there's two options: using a program called a "disk scrubber" or physically destroying the drive.
A disk scrubber is a program that over-writes the memory space in question with a garbage file. Most scrubbers do this multiple times to make it more likely that the data will be unretrievable. Physically destroying the drive can mean making holes in it with a drill, smashing it with a hammer, or even shooting it with a gun. Check this
article on Lifehacker for some good info on both methods.
To make your idea work, you could have your character try to use a disk scrubber but it's not thorough enough, or, better, they're interrupted before it's complete. Or have them try to destroy the disk physically but not do a good enough job.
The idea that they could recover five words, and somehow know that they're all from the same file and that file was an email, is pushing it. (I don't want to say it's impossible, because I'm not an expert on what law enforcement can do, but to my understanding of how data retrieval works it's highly unlikely.) I guess it depends how realistic you want to be. Tech experts do things in books all the time that are less realistic, though, so if it's integral to your plot, I think you could get away with it.
If you want a more plausable scenario, maybe law enforcement could recover, say, half a dozen emails, but only one is relevant to their case and the rest is the person sending cat pictures to their mum.
The computer experts were also able to figure out the real life, physical address of the person to whom the email was sent (or who sent it, doesn't much matter).
I know NOTHING about computers -- is this feasible?
To whom it was sent: not possible.
Who sent it: maybe, but it's not easy.
(The following assumes that the computer that sent the email isn't the computer that law enforcement have, i.e. that the computer received the email. Otherwise, you're back to not possible.)
Each computer on the internet is assigned an IP address. This is a series of numbers that looks like 208.77.188.166. Your IP address is assigned by your ISP, and some users, particularly those who have broadband, may have a fixed IP address. Others will be assigned a new IP address each time they log in.
When you send an email, your IP address is attached to the header, and with a typical email, law enforcement could see that easily. (You can see it yourself in your email program, usually by turning full headers on.) The problem I see here is that the email is almost totally deleted. They found only five words *and* the IP address? That's really, really pushing it.
Assuming it happened, though, here's what would happen next. Most ISPs will only give out who was using a particular IP address at a particular time with a court order. If your law enforcement folks could get that, you could get the address of the owner of the account that the IP address was assigned to.
But! All this assumes that the person was at their physical address at the time. Wired broadband access is typically linked to a physical address, and only works from that address (due to the way it's routed through phone or cable lines), but if your email-sender is using either dial-up or cellular internet then they could be anywhere. Whether you can see which cellular tower that connection was using like you can with a regular mobile phone call is not something that I know, though it certainly seems like it should be possible. Another possibility is that your user is using an open wireless network provided by a hotel, coffee shop, etc, in which case even when you trace it back to its location, you may be stuck trying to find out who the person was.
Hope that helps. I'm happy to answer further questions, if I can.
