There is a third possibility in the ZG5 world. Check out and make sure the VGA cable is in good condition and properly seated. See appropriate guides on this site to disassemble and re-assemble (and note - you don't have to completely disassemble to be able to see and reseat the motherboard side connector!). I have "repaired" two "broken" ZG5 screens by cleaning and reseating properly the motherboard side connector - cost: zero plus some of my time. This is definately the first to check. If the display does not get any better, the next step in my opinion is to replace the VGA cable. It gets constant wear and tear due to its positioning and either the wiring or the connectors could easily be broken so that the faut is not immediately noticeable. Cost is not so much, at least if you can salvage the cable from another broken ZG5.
There are two main types of Acer Aspire one ZG5. The first one is AAO110, which is the SSD model. The original SSD's are notorious for their poor speed, specifically writing speed is very poor. The AAO110 can use 1,3" and 1,8" ZIF PATA drives, e.g. some models used in Apple Ipods fit in as long as they are physically of right size. If the drive-to-be-installed is physically too big, you could consider removing gently some plastics of the netbook's case but beware - don't remove too much! Or in case it is a SSD, try to figure out how to remove possible casing (probably voiding the guarantee) and use the "bare" drive. The other main type is AAO150, which can use normal 2,5" SATA laptop hard drives and SSD's. For the AAO150 it is a lot easier to find suitable drives, they are practically everywhere.
In practise, ZG5 can only accept 1,5 gigabytes. This is due to following: (1) the chipset limitation is 2 GB (2) there is 512 MB (0,5 GB) RAM soldered onboard (3) there is only one memory slot So, if you add a memory stick of 256 MB (0,25 GB), 512 MB (0,5GB) or 1 GB you'll be fine as you don't exceed the chipset limitation. 1,5 GB memory sticks don't exist. If you add a stick of 2 GB (or more), you'll exceed the chipset limitation and your ZG5 won't boot. There are rumors of physically removing the original onboard RAM and then adding a 2 GB stick but I don't personally know anyone having done that. Anyway, I wouldn't recommend it, it would require some skills with soldering iron and such. I also have a vague memory of someone talking about newer ZG5 units having 0 or 1 GB onboard memory, so giving a possibility to reach the 2 GB limit, but I only have met older ZG5's with 512 MB onboard.
A quick addition to the answer: generally you can not upgrade or change a netbook processor. They are usually soldered to the main board and changing them would require special tools and skills. If you had both you would probably decide not to try because you would also know chances for failing and rendering the whole device useless are high. In addition to this, you would also need another CPU (processor), which you can not buy from the computer store next door like a new Phenom or Pentium for obvious reasons.