Sorry to hear that. On the off chance you give the game another try, I have some questions and feedback on your runs.
Eawyne: Okay, I tried, i did. But this is just not possible anymore... XD First run, first sector went fine. Ended it with enough scrap to purchase all I needed, and gained a nifty weapon (don't remember the name, the one that fires schrapnel-like rounds). I enter the second sector and after the second jump, I end up in a nebula. Double alarm ! I can't see anything inside my own ship, all systems are down and intruders are on board ! I'm stuck with only my three crew from the start and they die within a minute, as all systems were down, and I couldn't heal them.
Firstly, the flak cannon is awesome for taking down shields. Secondly, when you say purchased all that you need, what did you buy? Remember, in the first sector you should hold off on being too spend heavy at the stores unless you are purchasing certain systems or augments, as a lot of your scrap should go into upgrading your ship. Thirdly, if no ship was attacking you, it's always a good idea to move the crew and some energy from other systems into the medbay (assuming you have one) and vent the rest of the ship into space to make the invaders come to you and get slaughtered.
Eawyne: Second run. I didn't even finish the first sector ! I got stuck near a blasting sun, with a boarding party ! My weapons tore the enemy ship down, but my hull was heavilmy damaged, and the remaining boarding party finished the job...
Oh, the sun; those events can be a pain. That said, so long as you vent the rest of the ship into space (except for a path to the oxygen room so that repairs can be made by the crew without dying of oxygen deprivation), those fights get much easier; they can still be rough, though, especially if crew start teleporting in. In that happens, try disabling the enemy's weapons while keeping the enemy crew busy (sending people out to fight them to delay sabotage, send someone to the Doors subsystem room to make it harder for the invaders to leave vented rooms, etc.), then after the enemy ship is down, turtle up in the medbay.
Eawyne: Third run got me actually a jump away from the last sector, but bad luck didn't allow me to upgrade my weapons correctly, and I got myself stuck with a powerful vessel that ripped me apart. I managed to escape, only two crew left alive, and I ended up in a fight that finished me off.
When you say "upgrade my weapons correctly", what do you mean? Are you referring to the types of guns you had or the general capacity of the weapons system; if the former, what kinds of guns did you have on board? For that matter, what were the rest of your systems looking like? Remember that some guns work a lot better with some systems than others.