check the maps of a unit you might want to own to see if your small lakes are even in it or not. mine are not and so not worth owning an all in one with gps on screen. if i care to mark an area, i have my smart phone with gps, but i can always find my back because the lakes are so small.
screen size depends on how much graph info you want it to hold at any given time and how much more other information it can show along side the graph like marcum lx6/7/9 has for an example. these units show graph and flasher or graph and vertical displays with zoom in it's own dedicated chart/display. it can have up to four charts/displays at one time or all the way down to just one and has six to choose from and is designed for ice fishing first but can be used in open water with their high speed transducer sold separately. the mount it comes with can be used to hold it to your boat, it's aluminum.
sounds like their may be a funds issues being you mentioned an auction. that tells me you want a used unit and a deep discount. if so, these units do show up for sale used. they are a harder learning curve to get used to than say a three button vex so i think those for sale are because it's too much machine. on the other hand, it is much harder to out grow and offers so many tweaks and features.
because you mentioned screen size, i would presume you want a digital unit and you don't care about the other type, so you are versed in using digital units. this would be the choice i recommend for you. it also has 4 color palate choices including gray scale like their showdown has for color blind eyes and six color which is what i am used to coming from a humminbird ice-55 that also used 6 color.
new, you can get the 6 inch version (lx6s) for 550$ or so. their has been a 50$ price spike in these units over this summer.
as far as the display on your old unit goes, the back light burns out and is called a light engine. that's what lights up the pixels so you can see them. it may be a power source for it went bad or the light engine itself. check to see if every thing is tight that comes from the display to the board it runs to.
if your handy with meters you can measure the transistors if they are not SMD mounted, inspect capacitors and resistors and look for corrosion. if you want to learn electronics more, leave it plugged in for a final inspection and measure voltages feeding the display to make sure all of them have voltage and at least one should be a ground or no voltage. ground can be black in color. it's easy to discover what ground is because the ground circuit on the board is the largest in coverage on the copper side of the board and many of the components connect to it and you will see it soon after looking for it this way. also look for cold solder joints where the solder is not shiny and very dull in appearance. look for the lead to be only partially connected and maybe even loose.
if you can run it thru a search engine, you may find a typical problem that unit encounters and may be an easy fix or you might find out it's not worth the time of day to do any thing with it. you could call the manufacturer to see what they charge to get it back on it's feet and weigh your options after you have all the info you can find.
