You come up with a basic plan as you set oxygen level alarms for your suit. You'll try and see if you can get this ship's capacitor charged to the level of it starting up, and go from there. If that doesn't work, your plan B is to cannibalize the solar panels with tools if you can find them.
Much to your (relative) happiness, you seem to have parked your fighter close enough to the shuttle to be able to connect their batteries without moving something. You quickly rummage around in your ship for the cable and connect it to the capacitor's external port. Once this is done, you gently drag the other end of the rather bulky cable through the vacuum. You arrive again at the shuttle and start hoping that maybe, just maybe, there's a port for this type of connection.
There isn't. But there's something almost as good. On the outside of the ship near the engine, you find a small hatch covering a port that seems to be designed to take in electricity. If you were to find a screwdriver, you could disconnect the port covering and jury-rig an exposed connection. Sure, it wouldn't be safe, but neither is exploring an unknown space hulk in an unknown area of space.
You remember that there may have been some kind of tools in the shuttle's main cabin. You gently crawl across the shuttle's hull, but right as you start entering through the open door, your first oxygen alarm sounds.
"WARNING: Suit Oxygen at 33.3%. Estimated time until depletion: 10 minutes."
You carefully throw yourself away from the shuttle towards your fighter. You hit the shuttle and grab on within a minute, and crawl into the cockpit. You turn the life support back on and connect your suit to the port.
As you wait the minute needed to refill your suit's oxygen, you watch the capacitor level steadily go down. Eventually your suit reaches maximum capacity again and you disconnect it.
"Capacitor at: 22.5% of maximum capacity."
You start again. You re-enter the shuttle and scour the main cabin for any signs of a screwdriver. Just as you're about to give up, you see another (more obvious, somehow) panel on the wall next to the engine panel. Labeled "EMERGENCY". You easily open it, as it's on a hinge, and find...
Not much. A screwdriver and a wrench are latched in place with plenty of empty spots for other tools also present. Still a great find, though. You grab both the screwdriver and the wrench and clip them onto your suit.
"Suit Oxygen at 83.3%. Estimated time until depletion: 25 minutes."
You head back up to the external port where you left the cable floating. You unscrew the port's covering and carefully pry it off. On the inside of the port, you very carefully attempt to bend the connectors into the right shape. After a couple of minutes, you think you've managed to get them in the right shape. You plug in the cable and brace yourself for an explosion.
"Suit Oxygen at 70%. Estimated time until depletion: 21 minutes."
The shuttle immediately starts lighting up. You wait about 10 seconds and release the cable to avoid completely draining your fighter's capacitor.
You swing around the hull and enter the cockpit. This time, plenty of screens (that you can luckily read) welcome you.
From what you can tell...
The Capacitor is at 50% maximum charge.
All systems are completely functional.
There appears to be a basic orbital navigation system.
The fuel tank is at 100% capacity.
Life Support is online.
Life Support is using up around 10% of the capacitor just to run though and would pretty quickly exhaust it. Doesn't look like there are any other notable draws on power, though.
What now?
"Suit Oxygen at 63.3%. Estimated time until depletion: 19 minutes."