|The cmos battery is what determines whether your bios retains the time, date, and any other non default settings. When it starts to get too weak, you get time keeping problems like you describe. When it gets weaker yet or dies , the cmos won't be able to retain the non-default settings at all when the computer is not running, and you get a "Cmos Checksum Error" or similar message every time you boot after having shut down the computer, and you have to set at least the date and time.|
Your model may have a non-rechargable cmos button cell, which typically lasts for about 5 years, or a rechargable cmos battery, which may or may not last longer than about 5 years. In any case it sounds like yours needs to be replaced.
Take a look at the Dell Service Manual for your model - it probably shows you where it is and what type it is, and it may have the part number you need to search for.
Laptop main batteries work as they were designed to for about a year, then they begin to deteriorate - by the second year they cannot be charged to anywhere near their rated capacity, and it gets worse after that - e.g. they tend to short in places internally. If your main battery has never been replaced, you should replace it. In any case, eventually you'll have to replace it anyway - more recent laptops cannot run on the AC adapter alone - the battery has to be installed and be capable of being charged to at least a minimal capacity.
You do not necessarily have to buy a Dell main battery - there are lots of clones out there that are just as good and are much cheaper - typically Dell and other brand name builders warranty the main battery for only one year - most of the clones do too.
"...the monitor itself freaks out, starts shaking..."
That's a poor description - try again.
"... if you move the mouse the screen goes in the opposite direction .."
That's a video overlay mode - the video is displaying a screen resolution that's larger than the physical screen - when you move the mouse cursor closer to the edge of the screen, the whole display moves the opposite way the cursor is moving, within the limits of the larger resolution. I thought until recently that feature had gone the way of the dinosaur - e.g. a long time ago some ATI video drivers had that feature available (ATI called it a video overlay - other chipset makers may have called it something else) - but a friend showed me it recently she could enable that mode in XP with a recent video adapter. If your video never does that except after coming out of Standby or Hibernate modes, then my guess is you probably do not have the main chipset drivers loaded, and because of that Windows does not have the proper info to make coming out of Standby or Hibernate work properly.
Whenever you load Windows from a regular Windows CD (or DVD) from scratch, after Setup is finished you must load the drivers for the mboard, particularly the main chipset drivers, in order for Windows to have the proper drivers for and information about your mboard hardware, including it's AGP or PCI-E, ACPI, USB 2.0 if it has it, and hard drive controller support. If you have a generic system and have the CD that came with the mboard, all the necessary drivers are on it. If you load drivers from the web, brand name system builders and mboard makers often DO NOT have the main chipset drivers listed in the downloads for your model - in that case you must go to the maker of the main chipset's web site, get the drivers, and load them.