I'd try asking on the Plumbing Forum... Here is a link that might be useful: Plumbing Forum

Gina- It could be defective tubing or damage that occurred during installation and is just showing up now. Get a decent quality, stainless steel-braided hose to replace yours. I just got a new refrigerator and bought a new hose like that for the water supply. It cost less than $10 for a 5' hose.

Not a professional plumber, but here's what I would do: Make up an assembly of a quarter-turn stop, drop-ear fitting, and whatever length of PEX is necessary to mount the fitting on the wall AND reach where it will attach to your supply source. If you can't find 1/4 inch...use 3/8 or 1/2. The extra size will not cause a problem. Using whatever reference points are available, measure carefully to find a suitable location to drill from the basement, at an angle upward. A flexible electrical bit (Greenlee is one brand) may be of service. I would size my bit large enough so that after you insert the line from the top and complete the connections, you are able to insert the tip of a spray foam can (if you drill through an area which is insulated and inacessable) and spray from both the top and bottom, if necessary, to fill the void.

I like to have a half inch plumbing supply line in the wall, with the valve recessed into a small box and just about flush with the wall. If you choose a valve orientation that allows the connection to be made with the line parallel to the wall -- rather than having the line come straight out from the wall -- you will minimize the possibility of the line getting pinched when you shove the refrigerator in. Also, don't skimp on the length of the line since you want to leave yourself plenty of room to hook it up in the first place and to disconnect it if it ever has to be replaced. Just arrange it so that the line forms a big loop that will be pretty much up against the wall when the refrigerator is in place. I don't like to run line through cabinets because it is easier for it to be damaged or kinked from stuff getting shoved into the cabinets, and you still need enough slack behind the refrigerator to get at the line.