The ornamental design for an icechest with attachedumbrella holder, as shown and described.
FIG. 1 is a front perspective view of the ice chest with attached umbrella holder showing my new design;
FIG. 2 is a rear perspective view thereof;
FIG. 3 is top view thereof;
FIG. 4 is a bottom view thereof;
FIG. 5 is a front view thereof;
FIG. 6 is a rear view thereof;
FIG. 7 is a left side view thereof; and,
FIG. 8 is a right side view thereof.
The broken lines in the figures illustrate wheels that form no part of the claimed design. The broken lines inside the oval shape in FIG. 5 depict the boundary of the claim and form no part of the claim.