Two issues with a Vista laptop (screensaver + IP assignment)

So, I've got this laptop here that has Vista installed on it. I don't know if any of these problems are actually the fault of Vista or due to some other thing, but it's worth a mention.

a) For some reason, this laptop won't seem to initiate/stay in screensaver mode. I have it set up so that after 10 minutes of inactivity, the screensaver will kick in. Unfortunately, it never does. I'll leave an come back an hour later and the screen will be glowing brightly and I'll be confused as heck. Any idea what might be causing this?

I usually have the touchpad turned off, with a USB mouse plugged in.

b) Internet speed at home is kind of slow (wireless being even slower) so I usually have an ethernet cable plugged into the laptop all the time. Every time I turn off the laptop and then turn it on later, the internet fails to work unless I right-click on the connection, diagnose and repair, and automatically obtain new IP address. I have to do this every time, which kind of gets frustrating if I'm constantly moving the laptop around. The network settings are put to "automatically obtain new IP address" so I don't know how else to fix this.

Something I've thought of that may affect that: I usually use the laptop at home for Photoshop/Flash/whatever, so I've taken out the battery in favor of just using the charger (the battery only lasts for some 2 hours at best). Would this affect the screensaver or the IP address issue?

Jam it back in, in the dark.

Noticed a curious thing yesterday. I left foobar open and playing so I'd have some music while I worked on the PC, and the screensaver successfully kicked and stayed that way. When I stopped the music but left foobar open, it didn't kick in. Misuterii desu~ But that's okay, I'm more or less resigned to just closing the lid nowadays.

As for the internet dealie, I haven't tried unplugging/replugging, but I will next time it occurs.

There's nowhere I can't reach.