laptop keeps turning itself off during xp recovery program?

Sad to say, your "fixed" DC jack may still be the problem, particularly if your battery is dead. Here's why:

On a lot of laptop motherboards, the DC jack has a poor mechanical connection to the motherboard, to which it is delivering power. Sometimes, it is merely held on by a couple of stake posts pressed into holes in the fiberglass motherboard. It's pretty easy for the power cord to mechanically pull on the jack, until, through repeated use, it loosens these posts enough to crack the solder joints connecting the DC jack to the motherboard's power traces, often tearing the copper foil traces off the motherboard.

The only way to reliably repair this kind of board damage, is to replace the motherboard, which sometimes gets you an engineering revision in the form of an improved DC jack design. But nobody wants to pay for that kind of repair on a machine that is out of warranty. So, some technicians will try to glue the DC jack back on mechanically with SuperGlue or epoxy, and then make an electrical repair by trying to solder some short wires between fresh areas of the damaged foil traces on the motherboard, and the DC jack. It's a difficult kind of repair to do well, requiring a lot of mechanical preparation, patience, and some luck. It's easy to further damage the motherboard, so that it seems to be repaired, but within a few days of use, one or both electrical connections breaks again, at the repair site, leaving the motherboard in worse condition than it was before repairs were attempted.

I've probably seen 50 laptops, of various makes, with this kind of damage. Further attempts at motherboard repair for most of them was pointless -- there was just too much damage to the copper traces to make a reliable power connection. At that point, the only fix possible is replacing the motherboard. Most of these machine became parts donors for other machines.

The basic test for this is to take the battery out, turn the machine on with AC power, and gently wiggle the jack. If it drops out immediately, you've found your problem, again.

Compounding this, in your case, is that your battery was left uncharged for a year, meaning it is very likely dead recycle material. Lithium batteries age whether or not they are in use, but they age faster at room temperature, if not fully charged.

hey i suggest u stop using the lappie there might be a problem with one or maybe 2 of the fans in the lappie cozing it to shutdown to prevent further damage to the motherboard. this happens faster while gaming coz while gaming the lappie requires more processing and generates lot of heat cozing it to shutdown faster. the underside may remain cold because only one of the four fans might be damaged and some of the laptops have got settings that cause them to shut down even if one of the fans are not working when high processing is required. i recommend getting it checked by acer as i see it is still under warranty.