I can get someone to try and jump it again (maybe wait longer this time). The terminals looks fairly clean and it's clamped on well, but I can take the leads off and replace them. Maybe brush off the terminals too. Touching a single lead at a time with a wrench won't do anything bad, right? (as in won't shock me). Do I need to connect/disconnect them in any particular order?
@Eagle - are you saying I should take off the leads, then connect jumper cables (to battery or to leads?) and try to jump?
Getting some different advice here so I'm not sure what to do (and how to do it safely). Would like to avoid towing if possible and I need to get whatever done before work tomorrow evening.
The only way to shock yourself with 12v is to get really sweaty and then lay part of yourself (have had it happen to my stomach while basically lying on engines to reach stuff) across the terminals. All it is is a tingle...your body has too much resistance.
What you want to avoid is errantly wrenching on one terminal and swinging your tool (heh, 'swing your tool') into the other. Steel has a practical resistance of zero. You'll notice a large shower of sparks as a side effect of this.
Connect jumper cables to the dead car first (have the key off) and then to the live car, ground lead last. Ideally clamped to a good metal chunk of engine that's not by the battery, but no one listens to that rule. The risk of a small spark causing a hydrogen explosion that flings sulfuric acid everywhere is...well...possible. Has happened. But the battery needs to be getting overcharged like crazy (unlikely in a car if it has not been recently recharged by any external source).
Anyhoosits, if you make that last connection without exploding, start the good car up, then try the dead one. Sometimes it helps to have a helper crank it while you wiggle the cables to try and grind the little copper teeth into good contact with the battery terminal. Sometimes they just take a quick jiggle to get good contact.
Make sure the batt terminals are actually tightened, also. Just being 'on there' is often not good enough contact- if you can move the terminal on the post by hand (should feel rigid if you give it a light shake), they're loose.
If the car continues to not start, you'll need to check for voltage drop across the battery cables.