Hi all....
Hope someone can help. Been trying to solve for quite some time 
My Aspire 5745 laptop developed odd behavior (maybe not so odd if I knew what was going on). Here are the situations I've "tested":
1. Laptop boots fine (and runs great!) with only the battery installed (adapter unplugged).
2. If the adapter is plugged in (battery or no battery) it won't boot (at first, anyway...see No. 4A below) and the fan seems to come on at full speed as if the CPU has heated up for some reason.
3. Boot on battery and then plug in the adapter immediately, the computer freezes (and a reboot is needed).
4. Boot on battery and plug in the adapter *after* computer has been on for some time (5 or 15 mins.?) I can plug in the adapter and the computer works fine. In fact, if I shut down the computer and then turn it back on (w/adapter plugged in and battery installed) it boots fine (most of the time).
4A. Referring to Nos. 2 & 3 above...If I repeat No. 2, over time the laptop gets further and further into booting Windows (running Win 10) until it finally completely boots and runs great until I shut it down (it reboots fine, as well).
What I've checked/done:
1. Original adpater that came with laptop appears to output rated voltage even under load (when computer is running).
2. I've tried other adapters (of unknown quality...tho a couple were for HP laptops, and all were checked for output voltage) in case it was a noise issue. I'm about to build up a non-switching supply as another noise issue check.
3. I've dismantled the laptop to the point where I could check the battery/adapter switching circuit (on the motherboard) and as near as I can tell, the signals/circuitry is switching between battery and adapter as expected (when the adapter is plugged in, I can see the adapter voltage (~19.3V) on the main votage source. When using just the battery, I see the battery voltage (12.5V) on the main voltage source). Seems the CPU and other circuitry is working....at least as much as I can tell it is.
4. From schematics I can see that the only circuitry "unique" to the adapter side is the charging circuit (adapter drives, battery receives) and adapter/battery switching circuits (the 2 switching circuits have 1 common point which becomes the main power source for the laptop).
5. Upgraded the CPU from an i3-380 to an i5-560 on the off chance the CPU was somehow a source of the problem...it wasn't. I wanted to improve the laptop performance anyway.
My first guess was that it was some kind of heat issue in that things won't work when cold, but then start to as the laptop warms up. However, this happens ONLY when the adapter is plugged in (never a problem on battery only). Then there's the possibility it's still a noise issue. I've tried a few different power adapters (functional but of unknown quality) but the problem wasn't solved. Then I guess there's the possibility it's a bit of both (ugh!).
I realize some of this is kind of technical, so apologies to those who are unable to fully understand what I've done so far.
I'm thinking of buying a recovered motherboard to see if I can get the laptop back to functionality (actually, it's very functional once it's up and running...it's just getting there that's frustrating 
Didn't mean for this to go on for so long
If anyone has experienced something similar or has any ideas/suggestions that could help, I would appreciate it greatly. Thx.
Cheers....